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ASTROCLK Astronomical Clock and Celestial Tracking Program Page 69
CELESTIAL NAVIGATION
The close relationship between navigation and astronomy as
well as the development of accurate time keeping is no accident,
as related elsewhere in this text. In this age of constellations
of artificial navigation satellites (NAVSTAR Global Positioning
System) and precision inertial guidance or navigation systems
(INS), it is easy to forget how difficult navigation was when the
only "instrument" available may have been keen eyesight or a
simple compass. The captain of a modern ship or aircraft only
needs to glance at a digital readout to know his position within
a few meters. It has not always been so, and indeed the
occasional human or instrument failures which result in disaster
remind us that navigational skills (and common sense) still need
to be kept handy when traveling long distances.
Navigation, which might be defined as the skills required to
determine how to move from Point A to Point B, may be divided
into two reasonably distinct classes: visual and calculated.
Visual navigation is a skill we each practice every time we move
about; it involves those actions and reactions necessary to move
from our present location to a second location, whether across
the room or across town, which is always in view or via
intermediate way points always in view. Regardless of the
conditions or obstacles we encounter, we automatically make any
adjustments in our course required to keep us heading toward our
objective. The outcome is usually certain and we seldom think
much about the processes involved. Even longer distance travel by
automobile is primarily visual navigation, with occasional
reference to a map to remind us of the landmarks to watch for;
although some practice at map reading may be helpful, few
calculations are required.
True long distance travel, whether by land, sea, or more
recently in the air, requires navigation. The goal is to attain a
known destination which is not in view through conditions which
may be unknown or which may constantly be changing. Once again,
those of us who are merely passengers think little of the
processes involved. Unfortunately in a few cases, those charged
with our safety sometimes assume that Nature will unfailingly
cooperate and that they have correctly supplied all required
information to instruments which are (and will continue to be)
working perfectly. Airline pilots, ship captains, and weekend
sailors may occasionally fallen victim to these dangerous
assumptions with deadly results.
To be successful, any scheme of navigation must include
certain essential ingredients: the correct (UT) time, where you
are now, where you want to go, and how to measure or calculate
your progress towards that destination. The text which follows
describes two ingredients which are in common use today (if only
as backup skills in the event of electronic failure), "Navigation
by Dead Reckoning" and "Calculation of Position by Sight
Reduction".
ASTROCLK uses both of these methods to provide navigational
information and calculations. The equations required for these
calculations are given in the Nautical Almanac 1989 (see
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 70
BIBLIOGRAPHY). Beginning in 1989, the Nautical Almanac has
included a new section which describes the "Formulae and method
... for use with an electronic calculator or microcomputer for
the determination of position at sea". I have adapted this
material for use in ASTROCLK.
One final comment regarding ASTROCLK's navigation functions
is in order. So as to minimize the code and memory required to
perform these tasks, ASTROCLK utilizes common subroutines to
perform many of the calculations and display functions. These are
used for navigation and otherwise. In particular, navigational
positions may be shown to a precision of 0.01 seconds of arc and
such accuracy is far beyond even the most sophisticated satellite
navigation equipment today, never mind ASTROCLK. There are many
possible sources of error, both human and electronic, in the data
used for dead reckoning and celestial navigation, any one of
which could contribute a position difference of some minutes of
arc or more. I have made every effort to achieve reasonable
accuracy, but the user should keep possible error factors in mind
when using the navigation functions.
Setting UT TIME ZONE OFFSET
Prior to the inclusion of the Navigation Mode (Version 8943
and higher), ASTROCLK always assumed that the computer's internal
clock was set correctly to the local time and based all other
time calculations upon that assumption. Navigation, however,
presumes that the computer may be moving from place to place and
that the longitude (and therefore the local time and time zone)
may be changing. Under these circumstances, what ASTROCLK really
needs to know is Universal Time, UT1, and for our purposes UT =
UT1 = UTC to sufficient accuracy in most cases except extremely
precise navigation and astronomical measurements.
One way to accomplish that end is to simply set the
computer's clock to UT and be done with it; most users, myself
included, would object to that inconvenience especially when
using the computer outside of ASTROCLK. The alternative is to
introduce a constant which tells ASTROCLK how to calculate UT
from the setting of the computer's clock. I have chosen to use
the second method and to call the constant "UT TIME ZONE OFFSET".
When operated in this mode, the computer clock remains set to
"home" local time; UT time is always available by applying the UT
TIME ZONE OFFSET, and the correct local time is obtained directly
from the current longitude (either calculated or manually
entered). However, since local time is always calculated, no ZONE
CORRECTION is permitted in the Navigation Mode and any ZONE
CORRECTION in effect will be cleared when the UT TIME ZONE OFFSET
is set. For users accustomed to the "old" versions of ASTROCLK
(Versions 8935 and earlier) and who are not concerned with the
navigation features, program operation is essentially unchanged
and the ZONE CORRECTION is permitted if the UT TIME ZONE OFFSET
is left disabled (the default condition).
Several advantages result from the use of the UT TIME ZONE
OFFSET. Most importantly, ASTROCLK can always calculate UT time,
and therefore all of the celestial time and position information
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 71
regardless of the actual location of the user. Once properly set,
the user may "move" his computer from place to place and the time
will remain correct. Unlike operation in the normal real time
mode, the user may select another location using F6 and the
correct local time (as determined by the longitude) will be
displayed. By selecting a starting point (a navigational "fix")
and entering the true course and speed, the user may place
himself upon a moving vessel, calculate the current position by
dead reckoning (see following section), and maintain real time
coordinates for planetary or celestial bodies based upon the
current estimated position. Finally, the user may accurately
calculate his current geographic position using two or three star
sights, ASTROCLK's version of classical celestial navigation.
At the same time, several minor penalties must be paid for
these additional capabilities. First, as noted above, the ZONE
CORRECTION is not permitted. This may represent an inconvenience
for users in local time zones different from that calculated by
ASTROCLK. Second, for users with slower computers not equipped
with a math coprocessor, additional time is required for
calculations in all modes and performance for those computers is
slightly degraded. Performance degradation of AT and 386
computers, whether or not equipped with a math coprocessor, is
not significant. Last of all, additional RAM memory is required
for ASTROCLK to accomodate these features. [See the section
PROGRAM OPERATION, Required ASTROCLK Files, for additional
discussion.]
When ASTROCLK is first started, the UT TIME ZONE OFFSET is
disabled and program operation is essentially unchanged from
prior versions. The UT TIME ZONE OFFSET may be enabled or
disabled at any time by pressing Function Key F10 (NAVIGATION)
and then F10 again. If currently disabled, the main ASTROCLK
NAVIGATION menu will appear in the main window the first time F10
is selected:
ASTROCLK NAVIGATION INFORMATION
Navigation functions available are:
F1 = Show current NAVIGATION DATA
F5 = Select USNO Navigation Stars
Before using other NAVIGATION functions,
you must use F10 to set the time offset
between your computer clock and UT Time.
F10 = Set Computer UT Time Zone Offset
Select function or press RETURN to cancel:
Note that except for displaying current NAVIGATION DATA and
selecting USNO Navigational Stars, no other navigation functions
are available until the UT TIME ZONE OFFSET has been set. If the
UT TIME ZONE OFFSET is enabled, other functions will be available
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 72
for selection (see below). Pressing F10 the second time, to set
the UT TIME ZONE OFFSET, will display the following:
ASTROCLK NAVIGATION INFORMATION
In order to calculate positions and times
correctly, ASTROCLK must know the time zone
offset from UT Time to which your computer
is now set. If LOCAL and UT times are both
correctly displayed press '*'; otherwise enter
the time offset in hours. Press RETURN to skip
or F10 to disable UT OFFSET and NAVIGATION.
The current UT OFFSET is: (disabled)
Enter UT TIME ZONE OFFSET (hours):
The display reproduced above shows that the UT TIME ZONE OFFSET
is now disabled; if the UT TIME ZONE OFFSET were active, the
actual offset in hours would be displayed instead of
"(disabled)". If the local and UT times displayed in the small
windows on the right side of the screen are correct and no ZONE
CORRECTION is in effect, simply enter '*' (without the
apostophes) and ASTROCLK will calculate the offset. Otherwise,
enter the correct offset in hours followed by RETURN. Decimal
fractions of an hour are permitted. If the UT TIME ZONE OFFSET is
now active (a number such as "-7.00" is displayed instead of
"(disabled)") and you wish to disable the function, press F10
again. If you wish to retain the present value, press RETURN.
The required value for UT TIME ZONE OFFSET will be positive
for East longitudes and negative for West longitudes. For
example, the correct value is -8.00 for Pacific Standard Time or
-7.00 for Pacific Daylight Time and -5.00 for Eastern Standard
Time or -4.00 for Eastern Daylight Time. CAUTION: If your time
zone is non-standard (that is, if you must normally use a ZONE
CORRECTION to obtain the correct local and UT time displays), you
must enter the value that corresponds to your time zone as
calculated based upon your longitude and subtract an hour if
daylight time is in effect. Any ZONE CORRECTION in effect will be
cleared.
Verify that local time and UT time are both correct when
ASTROCLK resumes normal operation and repeat the process if
necessary. For locations with "standard" time zones, there will
be no apparent difference so long as the current longitude
remains in the original time zone. All standard time zones extend
7-1/2 degrees on either side of the 15 degree meridians. Once
set, the UT TIME ZONE OFFSET is saved in file ASTROCLK.INI and
will continue in effect until disabled.
You may verify the operation of the UT TIME ZONE OFFSET by
using Function Key F6. First, press "1" to select Local Time in
the main display window, then press F6. If you live in the
Western United States, enter "USNO" as the location and Eastern
Standard or Daylight Time will be shown, as determined by the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 73
current setting of the DAYLIGHT FLAG. If you live in the Eastern
United States, enter "RPV" as the location and Pacific Standard
or Daylight Time will be shown. Press F6 again and restore your
correct local name and coordinates and observe that the display
returns to your correct local time. UTC Time will not change as
you change location.
Even if you do not plan to use the other navigation features
of ASTROCLK, you may find it helpful to set the UT TIME ZONE
OFFSET. Once properly set, you may change ASTROCLK's local
coordinates using Function Key F6 to any desired location,
display the correct local time for that location, and view
planetary or celestial coordinates as they appear at that
location for the current time. For example, you may determine
where a particular object would appear in the sky (or if it is
below the visible horizon) at a given instant for Los Angeles,
Chicago, New York, London, and so forth. This may be done in real
time, or the clocks may be stopped and set to any desired time
and/or date.
Navigation by Dead Reckoning
The oldest and perhaps the most basic method of navigation
is called Dead Reckoning. The name derives from the fact that you
assume you are proceeding along the course you have "reckoned",
come what may. In theory it is quite simple: if you know where
you started and your course and speed, you may calculate your
present position; similarly, if you know where you are and where
you want to go, you may calculate the course, speed and time
necessary to get there. To improve accuracy, you may also take
into account the effects of wind, currents and other factors as
they occur. Provided all these things are known to sufficient
accuracy and are correctly included in your calculations, easy to
say but more difficult in practice, you will know your present
position and will likely reach your destination.
It is a considerable credit to the navigators of old that,
long before the development of the nautical chronometer, they
were able to sail for days and sometimes weeks relying entirely
upon dead reckoning and still come reasonably close to their
intended destination. Captain William Bligh, of "Mutiny on the
Bounty" fame (or notoriety, if you prefer), may never qualify as
Mr. Nice Guy but he nevertheless performed what must rank as one
of the most amazing feats of navigation ever recorded. This in
1789 by sailing a small boat on open seas nearly four thousand
miles from the point where he and 18 others were set adrift from
the Bounty all the way across the South Pacific to Timor in the
East Indies, arriving some six and a half weeks later. Even with
ASTROCLK along, I'm not sure I'd like to try to duplicate that
trick! Less spectacular but equally impressive feats were almost
a matter of routine for the master navigators of that age and
earlier.
ASTROCLK takes a somewhat simple minded approach to
navigation by dead reckoning. Four items of information are
required to specify the last "fix" or position from which future
movements are calculated: longitude, latutude, time, and date.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 74
The longitude and latitude may either be obtained from star
sights (as described in the following section) or be taken from
charts or other sources. CAUTION: West longitude and South
latitude are negative; not all sources use the same sign
conventions, particularly with respect to longitude. To avoid
confusion with respect to time zones, all navigational times and
dates are UT (Universal Time), still referred to by most
navigators as GMT or Greenwich Mean Time; even NASA retains the
older designation.
Once these data are entered, the current position is then
calculated by taking the true course and speed (in knots,
nautical miles per hour) and calculating the direction and
distance traveled in the time elapsed since the last position.
If the last position is accurate and if, as is less likely, the
course and speed correctly take into account all those effects
such as wind and current, the calculated position will be
accurate. Even when the current course and speed are less well
known, dead reckoning can provide a useful confirmation for other
methods of position determination.
ASTROCLK uses true bearings rather than magnetic bearings
since the magnetic declination, the difference between true North
and magnetic North as shown by a compass, varies considerably and
changes very slowly with time. The direction of the declination
is given as "East" or "West", meaning that true North is in the
specified direction from magnetic North. Magnetic declination
should not be confused with astronomical declination. In the
United States, the magnetic declination ranges from about 20
degrees West in the extreme Northeast to 22 degrees East in the
extreme Northwest. The line of zero magnetic declination, where
the true and magnetic bearings are the same, passes near Chicago,
Illinois and Tallahasse, Florida. Local magnetic anomalies can
also cause significant changes in the magnetic declination. Most
large ships and aircraft use satellite or inertial navigation
systems which provide true bearings but smaller craft (and the
air traffic control system) use magnetic bearings. Knowing the
local magnetic declination is therefore important in navigation
and can also be helpful for the alignment of telescopes when the
North star is not visible (i.e. during daylight hours).
When traveling long distances, life is not quite so simple
if the navigator wishes to minimize the distance covered. The
bearing or "true course" to a distant destination, that course
plotted directly on a conventional map or chart, does not
represent the ideal course. Depending upon the projection used in
the preparation of the chart, the minimum distance and best
course are not necessarily represented by a straight line. For
distances under several hundred miles, the difference is usually
trivial and can be ignored. However, for distances of hundreds of
miles or more which involve significant differences in longitude,
the navigator should plot his "great circle" course. A few
minutes spent with a globe and a piece of string stretched taut
between two locations will suffice to demonstrate that a great
circle route can be considerably shorter than what appears to be
the most direct route on a flat map. The polar route used by
aircraft from the Western United States to Europe is an example
of a frequently used great circle route. It is important to note
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 75
that, unlike lines of equal latitude, the meridians (lines of
equal longitude) are already great circle routes; therefore,
voyages which are primarily North-South gain little or no benefit
from plotting a great circle route.
Exactly following a typical great circle route involves
constant changes in course, since the route follows an arc rather
than a straight line when plotted on a standard projection chart.
In practice, therefore, navigators usually select a series of way
points along the desired route and follow a set course between
each point. The more way points selected, the better the
approximation to the great circle route -- and the greater the
chance for human error. It has been suggested that Korean Air
Flight 007 may have met disaster because of an entry error on a
way point, most likely a digit transposition in the longitude
coordinate, thereby crossing restricted Russian airspace rather
than being well out over the Pacific ocean and thus setting the
stage for what followed.
Although ASTROCLK calculates the distance already traveled
from the last navigation fix and the current position using dead
reckoning (current speed times elapsed time in the direction
specified by the current course), the distance to a selected
destination (or way point) is computed using the great circle arc
from the current position to that destination. To a first order
approximation, each degree of that arc is sixty nautical miles.
(The conversion is exact by definition along the equator but
becomes slightly less accurate as the latitude increases due to
the flattening of the Earth at the poles. ASTROCLK takes this
factor into account in its distance-to-destination calculations.)
The displayed distance to the destination is therefore always the
current great circle distance from the current position; whether
or not the destination lies along the present course is of no
consequence to the calculations, and that fact must be kept in
mind when using the data for navigation.
If the current speed is entered as zero, ASTROCLK may be
used to calculate the great circle distance from the current
navigation point to the selected destination. The distance is
shown in nautical miles and kilometers. Also shown is the "chart
course" from the navigation point to the destination.
By deliberately picking an off-course destination, you may
take advantage of this method and watch for the point of closest
approach as you pass by. By setting the speed to zero, which
forces the current position to remain at the navigation fix or
geographic location, ASTROCLK may also be used to calculate the
great circle distance between any two points on the globe.
Point-to-point navigation by either true or magnetic
bearings, as opposed to great circle routes, is most accurate in
the mid latitudes and over moderate distances. As the route
approaches polar regions and as the distances become longer,
inaccuracies become more and more significant; these inaccuracies
are almost entirely due to the coordinate system used to project
the surface of a sphere onto a flat surface. Since ASTROCLK and
most navigators use that same coordinate system, some care must
be used in these cases. The problem is easily illustrated by an
example: plot a straight line course of 45 degrees (Northeast) on
a typical Mercator or cylindrical projection of the world. Sooner
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 76
or later you will arrive at the top edge of the map, and that
entire upper edge represents the North Pole. Therefore, ANY
northerly course will eventually wind up at the North Pole; the
same applies with respect to the South Pole for southerly
courses. Transferring the plot to a globe will trace a gradually
curving course toward the pole. If the course were 80 degrees
rather than 45 degrees, it would trace a spiral route toward the
pole through successive revolutions around the globe.
Of course, no navigator would ever steer 80 degrees in hope
of eventually reaching the North Pole, but ASTROCLK must know how
to handle such a case in the event that a course is entered and
left alone for some days or even months. Having reached the Pole,
regardless of the circuitous route, the program must select a
reasonable and consistent method of processing continuing travel.
The most obvious choice is to assume that, having reached the
Pole, the voyage should continue on the opposite side of the
globe with a course 180 degrees different from the initial
course. Using this method, an initial course of 0 degrees (North)
will result in polar circumnavigation of the globe, just as
expected; reaching the North Pole, the course becomes 180 degrees
and continues to the South Pole where the process is reversed.
This is the algorithm which ASTROCLK uses over long distances but
it can yield results which appear rather peculiar taken out of
context.
When first started, the navigation functions of ASTROCLK
are disabled. Before attempting to enable these functions, the UT
TIME ZONE OFFSET must be set as described above. If the
navigation functions are enabled, they may be disabled at any
time by using Function Key F6 to enter new local coordinates.
This disables navigation without clearing the data; the
navigation data may be re-enabled with Function Key F10 followed
by F2 and then pressing RETURN to select the old data.
Once the UT TIME ZONE OFFSET has been set, pressing Function
Key F10 displays the full Navigation Menu:
ASTROCLK NAVIGATION INFORMATION
Navigation functions available are:
F1 = Show current NAVIGATION DATA
F2 = Set current NAVIGATION DATA
F3 = Set current DESTINATION DATA
F4 = Set current STAR SIGHT DATA
F5 = Select USNO Navigation Stars
F10 = Set Computer UT Time Zone Offset
Select function or press RETURN to cancel:
Pressing Function Key F1 will display the Navigation Data
now stored, whether or not navigation is active. A typical
display contains the following data:
ASTROCLK NAVIGATION INFORMATION
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 77
The current NAVIGATIONAL DATA are:
Nav LONGITUDE: -15.000000
Nav LATITUDE: 32.000000
Nav POSITION TIME: 20.0 UT
Nav POSITION DATE: 16-06-1989
Nav COURSE (true): 325.000000
Nav SPEED (knots): 20.00
DISTANCE Traveled: 10.00 nm = 18.53 km
ELAPSED TIME: 0.5000 hrs
Press RETURN to resume ASTROCLK:
When you have finished reviewing the data, press RETURN to resume
normal operation. You may use Function Key F7 to select the
preferred format of displaying angles and time.
Pressing Function Key F2 will display the current
navigational data as above except that the prompt at the bottom
of the window is changed to:
Press SPACE to enter NEW Navigation Data, or
press RETURN to ACCEPT, or F10 to CANCEL:
Press RETURN to accept the data as shown, press Function Key F10
to cancel data entry and return to normal operation, or press the
SPACE BAR to enter new or changed data. If you press RETURN, you
will be prompted for each of the six required items and the
current value of that item will be shown.
Nav LONGITUDE: -15.000000
Nav LATITUDE: 32.000000
Nav POSITION TIME: 20.0 UT
Nav POSITION DATE: 16-06-1989
Nav COURSE (true): 325.000000
Nav SPEED (knots): 20.00
If the current value of an item is correct, press RETURN for that
item. If you wish to change the item, enter the new value
followed by RETURN. The input format is very flexible, and the
longitude, latitude and course may be entered in degrees, degrees
and minutes, or degrees and minutes and seconds. Any item may
have a fractional decimal part. Use the comma as a separator. If
you wish to use the local coordinates and the current time as the
navigation fix, enter "*" (without the quotation marks) followed
by RETURN in response to the prompt for LONGITUDE. In this case,
only the COURSE and SPEED will remain to be entered.
When all items have been processed, the original display
will be repeated with any new or changed values shown and the
same prompt:
Press SPACE to enter NEW Navigation Data, or
press RETURN to ACCEPT, or F10 to CANCEL:
Press RETURN to accept the values shown and enable navigation or
press SPACE BAR if some values must be corrected. This process
may be repeated as many times as necessary and at any time. Once
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 78
the navigation functions have been enabled, the local coordinates
window will display the current calculated position based upon
the data just entered above using dead reckoning. If a non-zero
speed has been entered, the local coordinates window will display the
title "Calculated Position" instead of a location name, and that
position will be calculated in real time when the clocks are on.
The local time will be adjusted according to the current
longitude and all celestial and planetary positions and other
data will be calculated dynamically.
Once the navigation data has been entered, the main display
window may be set to the Navigation Mode by pressing the "N" key.
A typical navigation data display contains the following data:
ASTROCLK NAVIGATION INFORMATION
Data relative to: NAVIGATION DATA
LONGITUDE: -15 00'00.00"
LATITUDE: 32 00'00.00"
DISTANCE: 280.00 nm = 519.49 km
ELAPSED TIME: 14:00:00
Current COURSE: 325 00'00.00"
(No DESTINATION DATA entered)
In this example, Function Key F7 has been used to set the angle
and time formats as shown. Note that the distance traveled is
based solely upon the elapsed time multiplied by the current
speed and does not necessarily bear any relationship to the
distance between the navigational position or fix and the current
position. Note also that if the current speed has been set to
zero, the DISTANCE and COURSE data will not be displayed.
Even when actual navigation is not intended, ASTROCLK may be
used to measure great circle distances between the current
navigation point (or local coordinates) and any other geographic
location by setting the speed equal to zero. In this case,
certain items which do not apply, such as distance traveled, are
eliminated from the displays.
One final step is required to fully set up a navigation
or distance measuring situation: entering a "destination". The
destination may be the intended destination, a way point along
the projected course, or simply a point of interest. Two methods
are available for entering the destination data: Function Keys
F10 and SHIFT-F6; both methods accomplish the same purpose but by
slightly different techniques. To manually enter the destination
data, press F10 and then F3. The current destination information,
if any, will be displayed:
ASTROCLK NAVIGATION INFORMATION
Current DESTINATION DATA:
NAME: Way Point A
LONGITUDE: -15 14'57.84"
LATITUDE: 32 20'57.47"
You will be prompted in turn to enter new or changed information:
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 79
Enter NAME (SPACE to cancel):
Enter LONGITUDE (W = negative):
Enter LATITUDE (S = negative):
To clear all destination information, enter SPACE followed by
RETURN instead of a name or designation. Press RETURN to leave an
item unchanged. Note that West longitudes and South latitudes are
entered as negative numbers. The input format is very flexible,
and the longitude and latitude may be entered in degrees, degrees
and minutes, or degrees and minutes and seconds. Any item may
have a fractional decimal part. Use the comma as a separator.
Function Key SHIFT-F6 may also be used to enter destination
data, especially when that data is available in a "city file" on
disk. For example, file USWEST.VOR is available which includes
complete data for the 287 VOR's (VHF Omni-Directional Range, a
radio navigation aid for aircraft) in the 11 western states. A
navigator might wish to prepare a special file of navigation
points for use in an upcoming trip. Operation of SHIFT-F6 is
identical to that used to set the local coordinates with Function
Key F6.
Once destination data has been entered, pressing the "N" key
to enable the Navigation Mode will automatically include the
calculation of your present position compared to that
destination:
ASTROCLK NAVIGATION INFORMATION
Data relative to: NAVIGATION DATA
LONGITUDE: -15 00'00.00"
LATITUDE: 32 00'00.00"
DISTANCE: 280.00 nm = 519.49 km
ELAPSED TIME: 14:00:00
Current COURSE: 325 00'00.00"
Data relative to: WAY POINT A
LONGITUDE: -15 14'57.84"
LATITUDE: 32 20'57.47"
DISTANCE: 253.54 nm = 470.40 km
TIME TO DEST: 12:40:37
Chart COURSE: 140 04'26.57"
In this example, we have obviously sailed well past Way Point A
by some 254 nautical miles (great circle distance), and the
course back to that point as plotted on a conventional chart is
approximately 140 degrees. At the present speed, it would require
about 12 hours and 40 minutes to return to Way Point A IF we
follow the great circle route. For longer distances, the great
circle route and the chart course will NOT be the same, as
discussed above. For short and moderate distances, the two
courses will be approximately the same.
When the speed has been set to zero (using Function Key F2),
information which does not apply in that case is deleted from the
navigation mode display:
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 80
ASTROCLK NAVIGATION INFORMATION
Data relative to: NAVIGATION DATA
LONGITUDE: -120 34'00.00"
LATITUDE: 38 09'00.00"
ELAPSED TIME: 0:34:15
Data relative to: Crazy Woman, WY CZI
LONGITUDE: -106 26'06.00"
LATITUDE: 43 59'54.00"
DISTANCE: 727.77 nm = 1350.24 km
= 838.03 mi
Chart COURSE: 67 31'04.73"
In this example, the destination has been set to the aircraft VOR
at Crazy Woman, Wyoming (VOR code "CZI"), and the navigation fix
is for Calaveras County, California. Using SHIFT-F6, you may
select different destinations from the current city file and
obtain a display of the coordinates, distance and chart course
relative to the navigation fix. Note the addition of the distance
in statute miles ("mi") in this version of the display.
Celestial Navigation with Star Sights
To be effective, any method of navigation requires that the
initial position be known as precisely as possible. Departing a
location whose coordinates are known provides that initial data
but within a relatively short time, depending upon the speed of
travel, a navigator needs to determine a new position both to
check the accuracy of his dead reckoning calculations as well as
to serve as a new basis for position calculations. Failure to do
so can have unfortunate results.
One of the most accurate methods of establishing a position,
or "fix", has been to take sights of the Sun, Moon, planets or
selected bright stars, and use that information to compute a
position. This technique is known as celestial navigation. To do
this, a triangle known as the "celestial triangle" or
"navigational triangle" is formed between the observer, the North
or South Celestial Pole, and the selected star or other celestial
object. These three points are projected onto a sphere and the
solution of the angles of the resulting celestial triangle using
spherical trigonometry provides the position information the
navigator seeks.
A number of different methods have been used over past
centuries to obtain the solution to the celestial triangle. Early
methods were very cumbersome and difficult to solve accurately.
In the nineteenth century a technique called the Altitude-
Intercept Method was developed by the Frenchman Marc St. Hilaire
using two trigonometric equations (known as the Cosine-Haversine
formulas) to solve the problem. Although this new method was a
considerable improvement over earlier methods, it was still quite
a chore to manually calculate a position. About 1930 a Japanese,
Ogura, developed a simplified solution based upon sight reduction
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 81
tables. These tables gave the position of the Sun and selected
stars and planets at regular intervals throughout the year. By
recording the altitude of two or preferably three celestial
objects whose positions were tablulated, along with the time of
each measurement and the vessel's course and speed, the navigator
could determine his position at a specific time and calculate his
present estimated position.
The Nautical Almanac, jointly published every year by the U.
S. Naval Observatory and H. M. Nautical Almanac Office, gives
similar, improved tables today that form the basis for manual
calculation of a position by sight reduction. Data are given for
the Sun, Moon, Venus, Mars, and Saturn for each hour of each day,
and the positions of the 57 USNO navigational stars for each
three day period (since the rate of change of stellar positions
is relatively slow). The method involves little more than noting
the date and time, looking up numbers in the tables, and then
performing various interpolations, additions, and subtractions.
Simple as that may sound, the calculations must be performed
correctly and with sufficient precision in order to obtain a
reliable position.
With the advent of electronic calculators and, more
recently, portable computers, attention has again been focused
on St. Hilaire's original Cosine-Haversine formulas developed in
1875. Using the formulas directly instead of tables derived from
them makes electronic calculation relatively straightforward once
the formulas themselves have been properly entered. ASTROCLK uses
this method with observations of any of the 57 USNO Standard
Navigational Stars, as described in the Nautical Almanac 1989.
(However "straightforward" the data entry process may be, a brief
look at ASTROCLK's inner workings will reveal that setting up all
the information needed to use the formulas is a non-trivial
task!)
Regardless of which of these methods is employed, sight
reduction tables or formulas, everything depends upon taking
accurate star sights and knowing the correct time. Taking a
sextant sight on a moving vessel requires considerable skill and
practice as well as an accurate instrument. ASTROCLK and a good
short wave radio can provide the time to sufficient accuracy
almost anywhere in the world. The resulting position calculations
are more accurate than the typical star sights by an average
navigator.
Star sights are typically made using a marine sextant or a
bubble sextant. One of the important differences between these
two instruments is the method by which the horizon is determined.
The marine sextant uses the apparent horizon (which must
therefore be visible at the time of measurement) and the
resulting star altitudes must be corrected for "horizon dip", the
lowering of the apparent horizon as the elevation of the observer
increases. The bubble sextant, on the other hand, uses an
artificial (true) horizon formed by a bubble in a liquid, much
like the common carpenter's level, and needs no horizon
correction.
Depending upon the type of instrument being used, the
elevation must be set to the actual elevation of the observer's
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 82
eye above mean sea level (marine sextant) or to zero (bubble
sextant) using ALT-F6. ASTROCLK then makes the appropriate
correction for horizon dip using a standard formula. Failure to
set the elevation to the correct value can cause appreciable
position errors.
Some care should be used in the selection of the stars to be
used for celestial navigation. Since objects near the zenith
(directly overhead) are difficult to observe with a marine
sextant, they should be avoided; similarly, errors due to
refraction increase near the horizon. It is therefore recommended
that the selected stars be at observed altitudes of from about 15
degrees to 80 degrees.
Before the actual navigation calculations can be made, an
estimated position or navigational fix must be entered and the
celestial star sights must be taken. Using Function Key F7, set
the display format to your preference (i.e. the same format as
your sextant or navigational instrument uses). Then press
Function Key F10 followed by F2 (a combination referred to as
"Navigation Function Key F2") to enter the navigational fix data.
The longitude and latitude of the navigational fix need only be
entered to an accuracy of several degrees; a less accurate
estimate simply means a few more calculations for ASTROCLK to
achieve the desired accuracy. UT Time, UT Date, course and speed
complete the required items. If you are in a fixed position,
enter zero for course and speed. (See the Dead Reckoning section
above for a more detailed description of setting the navigational
fix.)
Taking an accurate star sight typically requires from five
to fifteen minutes. Record the UT Time when the sight is taken
along with the observed altitude. While you may wish to check the
azimuth of the star, ASTROCLK does not require that information
for its calculations. Star sights may be made before or after the
time of the estimated position.
HINT: If you set the estimated position as the current
coordinates using Function Key F6, you may then use ASTROCLK to
help select suitable stars for your location and time; select a
USNO Standard Navigational Star using Function Key F5 followed by
F1 and check the Target Tracking Display to see that it is
observable.
ASTROCLK internally "plots" each of your star sights to
determine a Line of Position (LOP) starting with the given
altitudes and times, and processes the internal star database
along with the course and speed to determine the various required
functions. The initial estimated position and calculated position
for each star sight should lie approximately along the Line of
Position. ASTROCLK then generates a calculated position from
these data and compares this calculated position with the initial
estimated position. If these differ appreciably, it substitutes
the new calculated position for the estimated position and
repeats the process until the difference in positions reaches a
minimum. The result is the final calculated position.
To begin ASTROCLK's celestial navigation calculations, press
Function Keys F10 and then F4. The program reminds you that you
must take either two or three star sights and have previously
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 83
entered your estimated position:
ASTROCLK NAVIGATION INFORMATION
Celestial Navigation requires observed data
for two or three USNO Navigational Stars.
For this data to be valid, you must first
have entered your last Navigation Fix using
Navigation Function Key F2.
Press RETURN to begin data entry or press
any other key to cancel:
Press RETURN if you are ready to enter the star sight data or
press any other key to cancel and resume normal program
operation.
After pressing RETURN, ASTROCLK requests that you enter the
instrument INDEX ERROR to be used in correcting the altitude
measurements:
Altitude measurements made with a sextant or
other instrument often have an associated
INDEX ERROR which must be removed from each
measurement prior to performing calculations.
Enter the INDEX ERROR (minutes) for your
instrument or press RETURN to enter zero.
The Index Error will be SUBTRACTED.
Enter Index Error:
Enter the index error in minutes of arc or press RETURN to enter
an index error of zero. Once you have entered an index error
value, ASTROCLK retains that value until the program is halted.
Note that the index error entered will be subtracted from your
altitude measurements.
ASTROCLK now requests that you select the USNO Standard
Navigational Star for the first star sight:
Select USNO Standard Navigational Star
Enter STAR NAME or STAR NUMBER:
You may enter either the star name, using upper or lower case and
sufficient letters to unambiguously identify the star, or the
star number, 1 to 57. Use "DENEB ", with a trailing space, to
select Deneb rather than Denebola. If you select star #49, for
example, the program will look up the star, display its full
name, and prompt you for the UT TIME of the star sight and the
observed altitude:
USNO Star #49 - a Lyrae - Vega
Enter UT TIME for Star Sight #1:
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 84
Enter Observed Altitude [Ho]:
ASTROCLK interprets any time entered as UT TIME, without adding a
trailing "U". The time may be before or after the time entered
for the navigation fix, but in practice the star sights should be
made at approximately the same time as the estimated fix in order
to minimize the dead reckoning errors if you are on a moving
vessel. The observed altitude is the reading directly from the
instrument; ASTROCLK will apply the horizon dip, index error and
refraction corrections automatically.
Repeat the last steps for the second (and third) star sight,
as prompted. If you are entering only two star sights, press
RETURN when requested for the USNO star number for the third
sight. ASTROCLK uses the least squares method of calculating the
position described in the Nautical Almanac 1989. However,
ASTROCLK uses its own internal algorithms to calculate altutides
and azimuths rather than those given in the NA; the results are
essentially the same using either method. While two "perfect"
sights are sufficient to do the calculations, three sights are
preferred to minimize potential errors. After a brief delay, the
results of the calculations are displayed:
The sextant altitudes have been corrected to:
Ho ALTITUDE 1: 20 02'31.94"
Ho ALTITUDE 2: 29 28'28.19"
Ho ALTITUDE 3: 43 55'22.80"
The Celestial Navigation calculations have
estimated the Navigational Fix Position as:
Nav LONGITUDE: -15 14'58.27"
Nav LATITUDE: 32 20'59.27"
Press RETURN to ACCEPT the calculated posi-
tion or any other key to discard:
The first section of data are the corrected values for the
observed altitudes. If data for only two sights have been
entered, no data will be shown for a third sight. The second
section of data are the results of the sight reduction
calculations: the calculated longitude and latitude.
If you wish to accept the new position, press RETURN; the
new position will then appear in the local coordinates window and
ASTROCLK will resume normal operation. Use Navigation Function
Key F2 to set the new position as the current navigation fix.
Selecting USNO Navigational Stars
Before star sights can be used with ASTROCLK's celestial
navigation functions, the two or three USNO Navigational Stars
must be selected. While the skilled star gazer or navigator will
immediately recognize the USNO stars, the casual observer may
have more difficulty. Navigation Function F5 scans all 57 USNO
stars, calculates the horizon coordinates (Altitude and Azimuth),
then displays the first 20 which may be found above 15 degrees
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 85
and below 80 degrees referred to the actual horizon. (Be sure
that the ELEVATION is correctly set!) All calculations are based
upon the current local coordinates and time.
In order to display this list, select Navigation Function
F5. A brief delay (longer for computers not equipped with a math
coprocessor!) will follow and then ASTROCLK will display the
selected stars. The first 20 stars which are suitable will be
displayed. Since the USNO stars are well distributed around the
celestial sphere, from 15 to 20 stars are usually acceptable at a
given time and place.
USNO STARS: 15 < ALTITUDE < 80
# ALT AZ MAG # ALT AZ MAG
3 67.1 5.1 2.2 | 47 21.7 318.4 2.2
4 38.0 174.7 2.0 | 49 22.3 302.7 0.0
6 65.6 108.5 2.0 | 51 22.5 265.6 0.8
8 43.1 120.6 2.5 | 53 46.2 302.5 1.3
9 53.8 50.0 1.8 | 54 45.9 246.7 2.4
10 31.8 90.7 0.9 | 56 23.2 200.8 1.2
12 34.9 54.0 0.1 | 57 63.9 229.5 2.5
13 16.2 93.2 1.6
14 27.1 72.2 1.6
40 20.7 350.1 2.1
Press RETURN to continue ...
The example above indicates that 17 USNO stars were considered
suitable for navigation purposes using the current local
coordinates and the current time. The following information is
displayed for each star: USNO number, Apparent Altitude (ALT,
degrees), Azimuth (AZ, degrees in the sense NESW), and standard
visual magnitude (MAG). The Altitude has been corrected for
refraction and horizon dip and therefore corresponds to the
apparent position in horizon coordinates where the star may be
found. Note that a star is brightest when its magnitude is
smallest; negative magnitudes are brightest of all.
Since the calculations are based upon the current location
and time, the navigator may use the current calculated position
or set an anticipated location and time (using F6 and F3) before
taking star sights and select "suitable" stars in advance. If the
current position is reasonably close to the expected position,
only the time need be set; this avoids disabling and then re-
enabling navigation mode when F6 is used.
The non-navigator may also find the display useful: by
setting the SPEED to zero (as discussed above), you may see an
immediate display of the current positions of the visible USNO
navigational stars (which also, by no coincidence, are the
brightest stars) visible at the current position and time. Star
gazers not yet accustomed to using horizon coordinates, altitude
and azimuth, may find the information helpful in orienting their
view of the night sky and in locating these stars.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 86
Celestial Navigation Example
It is often helpful to examine a worked out problem to see
how entries are made and calculations performed. The following
example illustrates how ASTROCLK can compute a position using
celestial navigation and is based upon the example on pages 282
and 283 of the Nautical Almanac 1989. The original objective, of
course, was to verify ASTROCLK's accuracy using known data.
1. Using Function Key F3, set the time and date to 20:00:00 UTC
("20U") on 16 June 1989 ("16,6,1989"). Note the "U" to
signify Universal Time.
2. Using Function Key F7, set the display format for degrees to
"ddd.dddddd" in order to agree with the format displayed in
the Nautical Almanac. (The display format makes no
difference to ASTROCLK.)
3. Using Function Key ALT-F6, set the Elevation to 0. Leave all
other local conditions at their default values.
In practice, the elevation should be be set to zero if the
instrument provides an accurate artificial horizon;
otherwise, set the elevation (height of the observer's eye
above mean sea level) so as to compensate for the dip of the
apparent horizon. The pressure and temperature should be set
to the current conditions, if known.
4. Using Function Key F10 followed by F2, set the navigation
fix to the coordinates, time, date, course, and speed
required. The following display should appear if all
information has been entered correctly:
ASTROCLK NAVIGATION INFORMATION
The current NAVIGATIONAL DATA are:
Nav LONGITUDE: -15.000000
Nav LATITUDE: 32.000000
Nav POSITION TIME: 20.0 UT
Nav POSITION DATE: 16-06-1989
Nav COURSE (true): 325.000000
Nav SPEED (knots): 20.00
DISTANCE Traveled: 0.00 nm = 0.00 km
ELAPSED TIME: 0.0000 hrs
Note that because the navigational fix time and date are the
same as the time and date set in Step 1, the calculated
distance traveled and the elapsed time are both zero.
5. Using Function Key F10 followed by F3, set the destination
name and coordinates. Use the following values:
Name: NA-1989
Longitude: -15.2494
Latitude: 32.3493
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 87
These values are the final position estimate calculated in
the Nautical Almanac and will be used to compare ASTROCLK's
position calculation. The destination information is not
required for ASTROCLK to perform the celestial navigation
calculations and it is included here only for purposes of
comparison.
6. Using Function Key F10 followed by F4, enter the star sight
information as follows:
Index Error: 0
Star #1: 49 (or "Vega")
UT Time: 20:00
Altitude: 20.08481
Star #2: 21 (or "Pollux")
UT Time: 19:50
Altitude: 29.50204
Star #3: 33 (or "Spica")
UT Time: 19:40
Altitude: 43.93917
Either the USNO Star Number or its proper name (sufficient
letters to unambiguously identify it, upper or lower case)
may be used without the quotation marks. The time entry does
not require the "U" to signify UTC. The altitude is shown
entered in degrees and decimal fraction, but may be entered
in any of the usual formats.
Note that if you were using an actual sextant, an index
error would normally be entered and automatically subtracted
from the measured altitudes. Once entered, the index error
is retained by ASTROCLK until the program is next restarted,
on the assumption that all altitude measurements will be
performed with the same instrument. The Nautical Almanac
example does not include any index error, hence no error is
entered here.
7. When the data have all been entered, the following display
will appear to enable you to check your data:
ASTROCLK NAVIGATION INFORMATION
The sextant altitudes have been corrected to:
Ho ALTITUDE 1: 20.042198
Ho ALTITUDE 2: 29.474503
Ho ALTITUDE 3: 43.923001
The Celestial Navigation calculations have
estimated the Navigational Fix Position as:
Nav LONGITUDE: -15.249526
Nav LATITUDE: 32.349772
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 88
Press RETURN to ACCEPT the calculated posi-
tion or any other key to discard:
The data input in Step 6 have been "rigged" to yield the
observed altitudes (Ho) in the display above. Comparison of
these corrected data with that published in the Nautical
Almanac will show a difference of no more than 0.000003
degrees, a trivial amount. The reason for rigging the data
is that the Nautical Almanac uses fully corrected data while
ASTROCLK automatically corrects the sextant altitude for
refraction. The input data have been adjusted so that the
observed altitudes agree after that refraction correction.
The second set of data are the position coordinates which
ASTROCLK has calculated from the input data. Press RETURN to
accept this position, or press any other key to discard the
calculation; either choice will return to ASTROCLK.
Accepting the data will change the local coordinates window
to the new longitude and latitude.
8. Now press "N" to change to Navigation Mode. The following
display will appear:
ASTROCLK NAVIGATION INFORMATION
Data relative to: NAVIGATION DATA
LONGITUDE: -15.249526
LATITUDE: 32.349772
DISTANCE: 0.00 nm = 0.00 km
ELAPSED TIME: 0.0000 hrs
Current COURSE: 325.000000
Data relative to: NA-1989
LONGITUDE: -15.249400
LATITUDE: 32.349300
DISTANCE: 0.03 nm = 0.05 km
TIME TO DEST: 0.0014 hrs
Chart COURSE: 165.108506
The first portion of the display shows the data relative to
the last navigation fix (which is the data ASTROCLK has just
calculated in Step 7) and is obvious. The distance and time
are both zero because ASTROCLK is set to the time of the
navigation fix. The course is as set in Step 4.
The second portion of the display shows the data relative to
the "destination", set to the results of the calculation in
the Nautical Almanac; note that the longitude and latitude
are exact. The distance is therefore the great circle
distance bewteen the fix ASTROCLK has just calculated and
the Nautical Almanac result, shown in nautical miles (nm)
and kilometers (km). In this case, ASTROCLK produced a
result within less than 200 feet of the Nautical Almanac.
Note that the initial position estimate entered in Step 4 is
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 89
quite close to the end result, following the example in the
Nautical Almanac. In fact, the estimated longitude and latitude
may be off by five or ten degrees in either direction with little
effect on the final result except to increase the computation
time on computers not equipped with a math coprocessor.
When using these celestial navigation functions, it is
important to note that the accuracy of ASTROCLK's calculations is
actually far better than can likely be achieved in practice. Not
only is it all but impossible to read a sextant or similar
instrument to the accuracy and precision used in the example, but
changing atmospheric conditions especially near the horizon
(which are difficult to measure from the Earth's surface without
a fully equipped observatory) can cause the refraction to vary by
as much as several arc seconds from the calculated value. The
purpose here is to provide a method which introduces little or no
additional error in the celestial navigation calculations. This
example demonstrates that ASTROCLK's apparent geocentric
equatorial star positions are typically within one arc second of
the values published in the Astronomical Almanac and the Nautical
Almanac as well as those generated by USNO's Interactive Computer
Ephemeris and Floppy Almanac, and that the resulting navigational
calculations are essentially exact.
For comparison with current state of the art navigation and
position determination equipment, manufacturers are claiming an
accuracy of better than 50 feet with military versions of the
NavStar Global Positioning System (GPS) receivers. Commercial
versions of the GPS receiver, which cannot decode some of the
special signals on NavStar (which are required for maximum
accuracy), are expected to achieve accuracies on the order of 300
feet or less.
In practice, ASTROCLK's navigation calculations can all be
made with the clocks running; the current calculated position is
displayed in real time and all celestial and planetary data are
similarly calculated. However in the case of this example from
the Nautical Almanac, because the date of June of 1989 is now
long past, the resulting calculated position after many months at
20 knots is not correct. By setting the computer clock and date
to some time shortly after the time of the last star sight (use
Function Key ALT-F4 to enable the SIMULATION mode, or use
Function Key F9 to return to DOS and then use the TIME and DATE
commands), the "real" situation can be simulated and the actual
running position will be displayed in the local coordinates
window, labeled "Calculated Position". At that point, you may
select a star or planet in the usual manner, display its
coordinates, and they will be referenced to the current
calculated position in real time.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 90
SIDEREAL TIME AND EQUATORIAL COORDINATES
The concept of sidereal time is perhaps a bit difficult for
the layman to grasp. Even the idea that time is not absolute may
be a little unsettling to some and confusing to others. However,
visualizing a "celestial sphere" with the Sun (heliocentric) or
the Earth (geocentric) at the center and with the stars, planets,
and other astronomical objects on its surface is relatively
straightforward. Using this approach, the stars remain in more or
less fixed positions on the sphere (although the planets
continuously change their positions) and the sphere appears to
rotate around us. Thus, stars appear to rotate about the
celestial pole in a counter-clockwise direction in the Northern
Hemisphere. Given this constantly changing scenario, astronomers
had to develop a coordinate system which would allow them to
unambiguously locate each celestial object. Although there are
several coordinate systems in use depending upon the application,
the most common is called Equatorial Coordinates and uses Right
Ascension and Declination, roughly analogous to geographical
longitude and latitude, respectively, to locate an object. This
is the coordinate system used in catalogs of star positions.
The problem, and the reason for sidereal time, is that the
Earth is rotating about its axis as it orbits the Sun. As a
result of this, when viewed at the same time each night the stars
appear to change their position by a small amount. After a full
year, they are back in their original positions. If we divide the
360 degrees around the celestial sphere into 24 hours (much the
same as our earthly time zones) and call the resulting coordinate
Right Ascension, we have described what is sometimes called "star
time" but is more properly termed Mean Sidereal Time.
(Declination, the second coordinate, specifies the number of
degrees above or below the celestial equator.)
Because of the Earth's rotation, sidereal time runs just a
bit faster than regular (mean solar) time; the difference is
about 4 minutes per day. If you are sufficiently patient, you can
watch one of ASTROCLK's sidereal clocks and see it skip a second
about every six minutes. Further, variations in the orbit and
rotation of the Earth and other considerations cause true
sidereal time not to be constant and astronomers therefore
usually use mean (or average) sidereal time.
The difference between solar and sidereal time is best
illustrated by an example. Remembering that the Earth makes one
complete orbit around the Sun in about 365 days, it follows that
the Earth moves through approximately one degree each day
(360/365). Since solar time is measured from noon to noon, the
Earth must therefore rotate through approximately 361 degrees
each day in order for a given point on the Earth's surface to
again be directly facing the Sun. But the sidereal day is the
time elapsed for the Earth to make exactly one revolution of 360
degrees. That one degree difference distinguishes the two methods
of time measurement and means that the solar day is about 4
minutes longer than the sidereal day (3 minutes 56.6 seconds mean
solar time, actually).
Both solar and sidereal time use the same units: days,
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 91
hours, minutes, and seconds; care must be taken that the type of
time being used is specified in order to avoid errors. The mean
sidereal times in ASTROCLK are calculated to a precision of
0.0001 seconds and have been checked against the Astronomical
Almanac for accuracy and are exact. All times displayed in the
small windows on the right of the screen have been rounded to the
nearest second. Near the vernal equinox each year (March 20th in
1988), sidereal time is exactly 12 hours different from mean
solar time. Similarly, sidereal time equals mean solar time near
the autumnal equinox in September.
The current sidereal time corresponds to the right ascension
that is on your meridian (the "line" running from the North
celestial pole to the South celestial pole and passing directly
overhead) at that instant. Therefore, if you know a star's right
ascension, you know that the star may be found somewhere on the
line from the North Pole through a point directly above you when
that right ascension equals the sidereal time. Where the star
will appear on that line is determined by its declination; +90
degrees corresponds to the North Pole, zero to the celestial
equator, and -90 degrees to the South Pole. If you hold your fist
out at arms' length with the thumb folded out of sight, its width
corresponds to about 10 degrees of arc (declination), or 40
minutes of time (right ascension) near the celestial equator. As
you move toward the poles, the lines of right ascension come
closer together, just as a section of orange is narrower at each
end. Another useful guide is that the stars most easily visible
at a given time will have right ascensions within a couple of
hours of the current sidereal time. Some stars, called
circumpolar stars, will always be visible if their declination is
greater than your latitude. If you stand at one of the poles,
naturally, all the stars you can see are circumpolar.
When you are far away from clocks, books, and program
ASTROCLK, you can estimate sidereal time or right ascension using
the two pointer stars of the Big Dipper; the right ascension of
both stars is very close to 11 hours. Using the meridian
connecting those two stars and the North celestial pole as a
starting point, you can imagine a "clock" in the heavens to tell
you the sidereal time and to estimate the right ascension of a
star. That's the good news; the bad news is that this simple
sounding analogy is complicated by the fact that the celestial
clock must be divided into 24 hours instead of 12 hours, and that
the hour numbers go around in the opposite direction from a
"normal" clock, or counter-clockwise. Even so, it's worth giving
it a try just to familiarize yourself with the concept and to
practice locating a few well known stars. See the following
section for the Equatorial Coordinates of a number of bright
stars selected by USNO as Standard Navigational Stars.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 92
USNO COMPUTER EPHEMERIS PROGRAMS
Beginning in the mid-1980's, the U. S. Naval Observatory
(USNO) supplemented its printed almanacs and ephemerides with a
disk-based program called the Floppy Almanac and designed to
execute on IBM-compatible personal computers (among others).
The Floppy Almanac was produced for years through 1999. While
not all Floppy Almanac data were equal in accuracy to that
contained in the Astonomical Almanac and other similar
publications, the Floppy Almanac provided more than sufficient
accuracy for most purposes and made reliable astronomical data
available to the vast majority of would-be users. USNO produced a
custom Floppy Almanac for each calendar year (400 days, actually,
with an small overlap from year to year).
Starting with 1988, all Floppy Almanac versions used a
common set of data files and by adding the custom Floppy Almanac
program for each year the user could produce astronomical data
for the years 1988 through 1999. One of the more useful features
of ASTROCLK (from my perspective, at least) is to automatically
execute the Floppy Almanac. When Function Key ALT-F9 is pressed,
ASTROCLK examines the current date, writes a default data file of
initial values, and then executes the proper version of the
Floppy Almanac.
The only significant problem with the Floppy Almanac has
been that each user must acquire a different version of the
program for each calendar year, plus or minus a few days. To
address this problem, USNO in early 1989 released a new program,
the Interactive Computer Ephemeris or ICE. ICE uses a common
program to process data for a 250 year period, from December 21,
1800, through June 7, 2049. A set of highly compressed ephemeris
data files (EPH01.DAT through EPH24.DAT), each covering
approximately 4000 days, allows the program to cover this
extended time span. For the approximate period 1980 through 1999,
only the data files EPH18.DAT and EPH19.DAT are required.
This added capability and convenience has its price,
however. Each data file (except the first and the last) requires
approximately 37K bytes of disk storage and the complete package
requires approximately 1.1M bytes of disk storage. The Floppy
Almanac for a given year, by comparison, easily fits on a single
360K byte floppy disk. Each time it is executed, ICE must select
and then decompress the appropriate ephemeris data file.
Particularly when executed on a computer without a math
coprocessor, ICE therefore runs more slowly than FA. ICE and FA
appear to have essentially the same accuracy.
In view of these factors, some users may may decide to
continue using the Floppy Almanac in preference to the
Interactive Computer Ephemeris. I have no information as to
whether or not USNO will continue to make the Floppy Almanac
available; I presently have FA versions for 1988 through 1992 and
these are available via my bulletin board system.
As of Version 8915, ASTROCLK allows the user to select which
USNO program will be executed via ALT-F9, or ALT-F9 may be
disabled if neither program is available. This selection is made
using ALT-F10. See the section SETTING PROGRAM OPTIONS for
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 93
additional information on using ALT-F10 to select the desired
USNO program and to set the proper drive and path names.
Both USNO programs operate in essentially the same manner.
Users familiar with the Floppy Almanac will have no difficulty
using ICE. The program name has changed, of course, and the
compressed ephemeris data files are a new fetaure. The star
catalog file names are unchanged and appear to be identical to
those supplied with the Floppy Almanac although the file dates
and times are different. The default parameter files, FA.DFT and
ICE.DFT, are slightly different; because of the time span
covered, the date parameter in the first line now requires the
full year for ICE. ASTROCLK correctly formats a default parameter
file for either program.
Each time ALT-F9 is invoked, the default parameter file,
ICE.DFT or FA.DFT, is written with the current ASTROCLK date and
time, the current local geographical coordinates, and the local
time zone referred to UTC; the parameters "Time Step" and "Num of
Positions" are each set to +1.00. The USNO program is therefore
ready to use immediately upon entry.
The following is a typical ICE.DFT file as written by
ASTROCLK (FA.DFT is the same except the Starting Date would read
"890328" rather than "19890328"):
Starting Date = 19890328.005806
Latitude = 38.150000
Longitude = -120.566667
Time Step = 1.0000
Num of Pos'ns = 1.0
Time Zone = -8.0
Use F1 after starting the program to adjust these parameters
if desired. See the User's Guide for each program for more
information on operation and features. Upon exit from ICE or FA
(using F10), ASTROCLK automatically resumes normal operation.
Operation of ASTROCLK with the USNO programs has been tested with
ICE Beta (test) version 0.50 and with FA versions 2.11.88 and
2.11.89.
If ICE has been selected (using ALT-F10), pressing ALT-F9
will automatically execute the ephemeris provided the current
date falls within ICE's time span and the proper ICE data files
are available. ICE may be used for any date from December 21,
1800 through June 7, 2049 inclusive. An error message is
displayed if the date falls outside these limits and ICE will not
be executed. The ICE ephemeris data files, EPH01.DAT through
EPH24.DAT, cover approximately 4000 days each; EPH18.DAT and
EPH19.DAT are sufficient for dates from about 1980 through 2000.
If FA has been selected (using ALT-F10), pressing ALT-F9
will automatically execute the Floppy Almanac if the current
ASTROCLK date falls within the years 1988 through 1999. An error
message is displayed if the date falls outside these limits and
FA will not be executed. (NOTE: ASTROCLK allows the use of FA88
for the last 15 days of December, 1987 and of FA99 for the first
15 days of January, 2000.) The proper Floppy Almanac program
(FA88.EXE through FA99.EXE) must be present in the ASTROCLK
directory or the Floppy Almanac drive and path must have been set
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 94
using ALT-F10, SETTING PROGRAM OPTIONS.
ASTROCLK assumes that neither ICE nor FA is present when it
is first started. Use ALT-F10 to first select the USNO ephemeris
program you desire, then to set the drive and/or path where the
program and its data files may be found. If the drive and/or path
for the selected ephemeris program is not set or is set
incorrectly, the ephemeris may fail to execute or it may warn the
user that it has used its internal default files. The default
selection for ASTROCLK is that both USNO programs are disabled
and ALT-F9 will have no effect.
NOTE: ASTROCLK remains in memory while ICE or FA is
executing; systems with less than 640K of main memory or which
have large Terminate and Stay Resident (TSR) programs active may
have insufficient memory for this feature. Also for this reason,
ICE and FA cannot be executed from ASTROCLK when using the
QuickBASIC interpreter rather than the complied program.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 95
USNO STANDARD NAVIGATIONAL STARS
The U. S. Naval Observatory (USNO) has designated 57 stars
as Standard Navigational Stars and publishes their coordinates
(along with those of other important stars) in a number of
their publications including the Almanac for Computers. For
convenience, I have added Polaris to the USNO list as number
zero. Throughout this text, the phrase "Standard Navigational
Stars" will mean the 57 USNO stars plus Polaris. The stars are
listed by Standard Navigational Star Number, Bayer Designation,
Proper or Common Name, Right Ascension (RA, hours), and
Declination (DEC, degrees). The Bayer designation consists of two
parts: a Greek letter, such as Alpha, to designate the particular
star in a constellation and usually in descending order of
brightness; and the name of the constellation in the Latin
genitive (possessive) case, such as Ursae Minoris and meaning "of
Ursa Minor". The names of the 88 constellations are always given
in Latin regardless of the origin of the name. Most of the common
names for stars are inherited from Arabic (the scientists and
mathematicians in North Africa being the conduit for much of our
knowledge of ancient astronomy and astronomers), with a few from
Greek and other languages. For an explanation and a listing of
constellation names, see the following section CONSTELLATIONS AND
NAMES.
The actual star data has been extracted from the USNO Floppy
Almanac 1988, Version 2.11.88, file STAR1.CAT, and is for Epoch
J2000.0. Not shown in the table below but included within the
program are constants for adjusting the data for proper motion.
The data represent the "mean place" of the star, described by
USNO in the Almanac for Computers 1988 as "a fundamental
reference point with no simple geometric or observational
significance. The apparent place of a star is the geocentric
position, referred to the true equinox and equator of date, at
which the star is observed. Thus, the apparent place is the
position needed for navigation, calibration of telescope setting
circles, computation of transit time, etc." Star catalogs with
earlier epochs, such as B1950.0, use "mean catalog place" which
has a slightly different meaning.
# Bayer Designation and Name RA DEC
----------------------------------------------------------------
0 Alpha Ursae Minoris, Polaris 2.530195556 89.264088889
1 Alpha Andromedae, Alpheratz .139795833 29.090438889
2 Alpha Phoenicis, Ankaa .438063889 -42.306058333
3 Alpha Cassiopeiae, Schedar .675125000 56.537350000
4 Beta Ceti, Diphda/Deneb Kaitos .726492222 -17.986616667
5 Alpha Eridani, Achernar 1.628570000 -57.236716667
6 Alpha Arietis, Hamal 2.119556389 23.462405556
7 Theta1 Eridani, Acamar 2.971026667 -40.304713889
8 Alpha Ceti, Menkar 3.037992500 4.089702778
9 Alpha Persei,Mirfak 3.405379167 49.861205556
10 Alpha Tauri, Aldebaran 4.598676944 16.509275000
11 Beta Orionis, Rigel 5.242296667 -8.201661111
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 96
# Bayer Designation and Name RA DEC
----------------------------------------------------------------
12 Alpha Aurigae, Capella 5.278153611 45.998027778
13 Gamma Orionis, Bellatrix 5.418849167 6.349650000
14 Beta Tauri, Elnath 5.438197500 28.607408333
15 Epsilon Orionis, Alnilam 5.603558056 -1.201950000
16 Alpha Orionis, Betelgeuse 5.919529722 7.407041667
17 Alpha Carinae, Canopus 6.399199722 -52.695694444
18 Alpha Canis Majoris, Sirius 6.752464167 -16.716108333
19 Epsilon Canis Majoris, Adhara 6.977096667 -28.972083333
20 Alpha Canis Minoris, Procyon 7.655031389 5.225016667
21 Beta Geminorum, Pollux 7.755262778 28.026183333
22 Epsilon Carinae, Avior 8.375231389 -59.509586111
23 Lambda Velae, Suhail 9.133271111 -43.432605556
24 Beta Carinae, Miaplacidus 9.219988056 -69.717208333
25 Alpha Hydrae, Alphard 9.459790833 -8.658652778
26 Alpha Leonis, Regulus 10.139531944 11.967191667
27 Alpha Ursae Majoris, Dubhe 11.062129444 61.750894444
28 Beta Leonis, Denebola 11.817661111 14.572041667
29 Gamma Corvi, Gienah 12.263435000 -17.541936111
30 Alpha1 Crucis, Acrux 12.443297500 -63.099050000
31 Gamma Crucis, Gacrux 12.519424722 -57.113194444
32 Epsilon Ursae Majoris, Alioth 12.900485556 55.959852778
33 Alpha Virginis, Spica 13.419885278 -11.161308333
34 Eta Ursae Majoris, Alkaid 13.792342778 49.313319444
35 Beta Centauri, Hadar 14.063724444 -60.372997222
36 Theta Centauri, Menkent 14.111375278 -36.370008333
37 Alpha Bootis, Arcturus 14.261021389 19.182419444
38 Alpha Centauri A, Rigil Kentaurus 14.659968056 -60.835400000
39 Alpha2 Librae, Zubenelgenubi 14.847975833 -16.041783333
40 Beta Ursae Minoris, Kochab * 14.845096111 74.155494444
41 Alpha Coronae Borealis, Alphecca 15.578132222 26.714705556
42 Alpha Scorpii A, Antares 16.490121944 -26.431986111
43 Alpha Triangulii, Atria 16.811074722 -69.027727778
44 Eta Ophiuchi, Sabik 17.172966944 -15.724919440
45 Lambda Scorpii, Shaula 17.560148333 -37.103811111
46 Alpha Ophiuchi, Rasalhague 17.582243333 12.560038889
47 Gamma Draconis, Eltanin 17.943435278 51.488947222
48 Epsilon Sagittarii, Kaus Aust. 18.402868611 -34.384647222
49 Alpha Lyrae, Vega 18.615647778 38.783658333
50 Sigma Saggittarii, Nunki 18.921090000 -26.296730556
51 Alpha Aquilae, Altair 19.846389444 8.868341667
52 Alpha Pavonis, Peacock 20.427458889 -56.735105556
53 Alpha Cygni, Deneb 20.690532500 45.280363889
54 Epsilon Pegasi, Enif 21.736434444 9.874977778
55 Alpha Gruis, Al Na'ir 22.137222222 -46.960997222
56 Alpha Piscis Austrini, Formalhaut 22.960848611 -29.622250000
57 Alpha Pegasi, Markab 23.079349444 15.205250000
* The Right Ascension for Beta Ursae Minoris, #40, appears in
error but is correct. The USNO J1988.5 list was in strict
descending order of SHA (Sidereal Hour Angle, directly related to
RA) but proper motion and precession changes to J2000.0 have
changed the RA. To avoid possible confusion, I have retained the
original USNO order and numbering (Almanac for Computers, 1988).
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 97
CONSTELLATIONS AND NAMES
One of my early "novice" problems when trying to identify a
star or constellation was to learn the names of the various
constellations and their standard 3-letter IAU abbreviations.
Some were easy to guess but others were less obvious and it was
some time before I discovered a reference with the proper
information. There are still a few that I have not yet memorized.
I have divided the list which follows into three sections,
Northern, Zodiacal, and Southern. The Northern and Southern
designations correspond roughly to the location of the
constellations with respect to the celestial equator. The twelve
constellations of the zodiac, of course, are closely linked with
astrology, a "science" once considered a part of astronomy, and
span a band of approximately eight degrees on either side of the
ecliptic following the course of the Sun through the heavens. The
names marked with an asterisk are those known to the Egyptian
astronomer Ptolemy and, for the most part, the ancient Greeks;
many of these names have survived essentially unchanged for two
thousand years and more although all 88 constellations are now
known by the Latin version of their names, whatever the origin.
To the ancients, and continuing almost to modern times, the
constellations were more or less casual groups of stars usually
clustered around one of the brighter stars easily visible to the
naked eye. Descriptions of the ancient Greek constellations are
found in the poetry of Homer (9th century B.C.) and Aratus (3rd
century B.C.). Ptolemy (2nd century A.D.) cataloged about 1022
stars, divided into 48 different constellations, that could be
seen from Alexandria. His chief work, the Almagest, remained the
definitive authority until the European voyages of discovery in
the sixteenth century brought navigators into Southern latitudes.
The first star atlas, published by Johann Bayer in 1603, employed
a method of identification still in use today and added 12 new
Southern constellations.
During the three hundred plus years which have followed
Bayer, more constellations have been added to the list, old
constellations have been split into several new groupings, and
new names have been adopted or proposed. Some of these changes
stuck, some did not. Since about 1750, no changes to the
constellation names have been accepted except that since about
the mid-1800's Ptolemy's constellation Argo Navis (Argo the Ship)
has usually been divided into three parts representing the keel
(Carina), the stern (Puppis), and the sails (Vela). The compass
(Pyxis) is also sometimes considered part of the original Argo
Navis.
With the advent of the telescope, many more stars were
visible and the practice of naming and cataloging stars according
to the constellation in which they appeared continued.
Unfortunately, the boundaries of the constellations were not well
defined and there was occasional confusion. The boundary problems
were codified in 1930 when the International Astronomical Union
(IAU) agreed upon precise definitions. The new divisions were
drawn along lines of right ascension and declination for Epoch
1875.0 and were made to zigzag in order to retain the ancient
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 98
figures. One result of this new precision, however, was that a
few stars previously known as part of one constellation became
part of another. For example, one of the four stars of the Great
Square of Pegasus became part of the constellation Andromeda and
is now known as Alpha Andromedae. Because of precession since
1875, the boundary lines are no longer nicely aligned with the
coordinate scales.
Only a few stars have a common or proper name such as
Polaris or Arcturus. The remaining stars, those few out of the
uncounted billions that have names or numbers at all, were named
by the individuals who cataloged them. Since there are many
different catalogs, stars often have multiple names, another
source of possible confusion and errors. One catalog often
includes a star or other objects with coordinates very slightly
different from a comparable object in another catalog, probably
the same object but not always. More confusion!
Many different methods have been used to name or number
stars, but one of the most common is still the Bayer designation.
Each star in a constellation was assigned a Greek letter, usually
starting with the brightest (alpha), and the name of the
constellation was appended. The Greek letter may be followed by a
superscript to distinguish multiple stars. The constellation name
is used in the Latin genitive (possessive) case, meaning "of" or
"belonging to". Thus the first and brightest star of the
constellation Andromeda is Alpha Andromedae, and in Ursa Minor we
have Alpha Ursae Minoris (Polaris), and so forth. In most
references, however, both the Greek letter and the constellation
name are abbreviated.
The first three lists show the standard IAU abbreviation,
Latin constellation name, Latin genitive name, and common English
translation for the three groups of constellations. The final
list gives the standard abbreviations for the letters of the
Greek alphabet. Using these lists, the abbreviated Bayer
designation of a star can easily be "decoded"; for example, OMI
CVN is Omicron Canum Venaticorum.
NORTHERN CONSTELLATIONS (28)
AND *Andromeda Andromedae Andromeda
AQL *Aquila Aquilae Eagle
AUR *Auriga Aurigae Charioteer
BOO *Bootes Bootis Herdsman
CAM Camelopardis Cameloparids Giraffe
CVN Canes Venatici Canum Venaticorum Hunting Dogs
CAS *Cassiopeia Cassiopeia Cassiopeia
CEP *Cephus Cephi Cephus
COM Coma Berenices Comae Berenices Berenice's Hair
CRB *Corona Borealis Coronae Borealis Northern Crown
CYG *Cygnus Cygni Swan
DEL *Delphinus Delphini Dolphin
DRA *Draco Draconis Dragon
EQU *Equuleus Equulei Little Horse/Colt
HER *Hercules Herculis Hercules
LAC Lacerta Lacertae Lizard
LMI Leo Minor Leonis Minoris Little Lion
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 99
LYN Lynx Lyncis Lynx
LYR *Lyra Lyrae Harp
OPH *Ophiuchus Ophiuchi Ophiuchus
PEG *Pegasus Pegasi Pegasus
PER *Perseus Persei Perseus
SGE *Sagitta Sagittae Arrow
SER *Serpens Serpentis Serpent
TRI *Triangulum Trianguli Triangle
UMA *Ursa Major Ursae Majoris Big Bear
UMI *Ursa Minor Ursae Minoris Little Bear
VUL *Vulpecula Vulpeculae Little Fox
CONSTELLATIONS OF THE ZODIAC (12)
AQR *Aquarius Aquarii Water Bearer
ARI *Aries Arietis Ram
CNC *Cancer Cancri Crab
CAP *Capricornus Capricorni Goat
GEM *Gemini Geminorum Twins
LEO *Leo Leonis Lion
LIB *Libra Librae Scales
PSC *Pisces Piscium Fish
SGR *Sagittarius Sagittarii Archer
SCO *Scorpius Scorpii Scorpion
TAU *Taurus Tauri Bull
VIR *Virgo Virginis Virgin
SOUTHERN CONSTELLATIONS (48)
ANT Antlia Antilae Pump
APS Apus Apodis Bird of Paradise
ARA *Ara Arae Altar
CAE Caelum Caeli Chisel
CMA *Canis Major Canis Majoris Big Dog
CMI *Canis Minor Canis Minoris Little Dog
CAR Carina Carinae Ship's Keel
CEN *Centaurus Centauri Centaur
CET *Cetus Ceti Whale
CHA Chamaeleon Chamaeleonis Chameleon
CIR Circinus Circini Compass
COL Columba Columbae Dove
CRA *Corona Australis Coronae Australis Southern Crown
CRV *Corvus Corvi Crow
CRT *Crater Crateris Cup
CRU Crux Crucis Southern Cross
DOR Dorado Doradus Swordfish
ERI *Eridanus Eridani River Eridanus
FOR Fornax Fornacis Furnace
GRU Grus Gruis Crane
HOR Horologium Horologii Clock
HYA *Hydra Hydrae Water Snake
HYI Hydrus Hydri Water Snake
IND Indus Indi Indian
LEP *Lepus Leporis Hare
LUP *Lupus Lupi Wolf
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 100
MEN *Mensa Mensae Table
MIC Microscopium Microscopii Microscope
MON Monoceros Monocerotis Unicorn
MUS Musca Muscae Fly
NOR Norma Normae Level
OCT Octans Octantis Octant
ORI *Orion Onionis Orion
PAV Pavo Pavonis Peacock
PHE Phoenix Phoenicis Phoenix
PIC Pictor Pictoris Easel
PSA Piscis Austrinus Picis Austrini Southern Fish
PUP Puppis Puppis Ship's Stern
PYX Pyxis Pyxidis Ship's Compass
RET Reticulum Reticulii Net
SCL Sculptor Sculptoris Sculptor
SCT Scutum Scuti Shield
SEX Sextans Sextantis Sextant
TEL Telescopium Telescopii Telescope
TRA Triangulum Australe Trianguli Australis Southern Triangle
TUC Tucana Tucanae Toucan
VEL Vela Velorum Ship's Sails
VOL Volans Volantis Flying Fish
GREEK LETTER ABBREVIATIONS
ALP Alpha NU Nu
BET Beta XI Xi
GAM Gamma OMI Omicron
DEL Delta PI Pi
EPS Epsilon RHO Rho
ZET Zeta SIG Sigma
ETA Eta TAU Tau
THE Theta UPS Upsilon
IOT Iota PHI Phi
KAP Kappa CHI Chi
LAM Lambda PSI Psi
MU Mu OME Omega
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 101
USING EXTERNAL STAR CATALOGS
ASTROCLK stores all the data for the 57 USNO Standard
Navigational Stars plus Polaris internally. USNO has prepared a
catalog, STAR1.CAT, of 1536 bright stars (the first 57 of which
are the Standard Navigational Stars) in conjunction with their
Floppy Almanacs. This catalog is from the Fifth Fundamental
Catalog, FK5, with one star (Eta Ophiuchi) added. A second USNO
catalog, MESSIER.CAT, contains data for the 109 standard Messier
objects; M40 has always been "missing" but an entry with null
data occupies its place in the catalog. All catalog data is for
Epoch J2000.0.
These two USNO catalogs have been converted to an ASCII
format (using the USNO program CATALOG) and combined to form
ASTROCLK.CAT with a total of 1645 stars and objects included. The
catalog is fairly large, requiring approximately 160K of disk
space. For those users short of space and who might wish to omit
the catalog from their disk, ASTROCLK will issue a warning
message if a search is requested and ASTROCLK.CAT cannot be
found; press RETURN to resume normal operation. The Messier
catalog is also available separately in ASCII format as
MESSIER.CAT.
ASTROCLK can perform two types of catalog searches: search
for USNO Name or Number or, search for star closest to specified
RA/DEC or ALT/AZ position as selected by Function Key F5 followed
by F3, F4, and F5 respectively.
Each entry in the catalog is assigned a "catalog number"
corresponding to its position in the file. If you wish to examine
the whole file, you may print it with your favorite print utility
(adding sequential line numbers, if desired) or look at it with
your favorite editor. The names assigned by USNO follow standard
IAU conventions but may take a bit of getting used to for the
novice user.
USNO allows up to three different 8-character names for each
star. In the following explanation each type of name is followed
by an example in parenthesis. The first name is either the Bayer
Designation (BET AND or ALP2 LIB) if one has been assigned to
that star, or the Messier Number (M 23). The second name, if any,
is the common name usually associated with the star (Polaris) or
the NGC number for the Messier object (NGC 1976). The third name
is the DM Number (Bonner Durchmusterang Catalogue) for the star
(-15 3996) or the common name for the Messier object (Orion).
Note that a SPACE is required between two part names. Many stars,
particularly those toward the end of the STAR1.CAT catalog, have
only the DM Number as a name and a printout of the catalog is
almost essential if these stars are to be used with ASTROCLK. Any
name field may be left blank and names have been truncated to 8
characters if necessary.
Press F3 to search by name or number. After the requested
name or number has been entered, ASTROCLK will capitalize the
name and adjust the spacing if necessary to that required by the
catalog. ASTROCLK then locates the catalog file (ASTROCLK.CAT
unless another catalog has been designated using ALT-F10). If a
catalog number has been entered, ASTROCLK reads the corresponding
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 102
data immediately; when a name is entered, a search of the catalog
is required. Floppy disk based computer systems may notice a
considerable delay for stars located near the end of the catalog
and for searches which require testing the whole catalog. For
floppy disk systems and slower hard disk systems, a considerable
improvement in search time can be obtained if you have sufficient
memory and use a "RAM DISK" to store the catalog and specify the
new drive and name using Function Key ALT-F10.
Searches by ALT/AZ or RA/DEC also search the entire catalog;
F4 is used for RA/DEC (Right Ascension and Declination), and F5
for ALT/AZ (Altitude and Azimuth). Pressing F4 gives the follwing
prompt (F5 is the same except ALTITUDE and AZIMUTH will be
requested):
SET TARGET COORDINATES
Search external STAR CATALOG for nearest
star using Right Ascension & Declination:
Enter RIGHT ASCENSION (hours):
Enter DECLINATION (degrees):
Show nearby star list [Y/n]:
Enter the coordinates as requested. Searches can be made in two
modes: find the 10 stars nearest to the coordinates given, or
find the single star nearest to the coordinates given. The search
mode is determined by the third prompt: "Y" (or RETURN) will find
10 stars and display a list of those stars; "N" will find the
nearest star and immediately switch to the Target Tracking
Display. Searches for a single star are somewhat quicker than
searches for 10 stars, due to the additional sorting required.
The following is a typical list of 10 stars (the degree symbol
has been omitted):
CAT # Diff RtAscension Declination Mag
49 0.04 18:36:56.33 38 47'01.16" 0.0
536 4.33 18:19:51.70 36 03'52.43" 4.3
1050 5.30 18:15:38.79 42 09'33.61" 5.6
208 6.00 18:50:04.80 33 21'45.65" 3.5
390 6.23 18:55:20.11 43 56'46.00" 4.0
894 6.57 19:07:18.12 36 06'00.61" 5.3
1593 6.63 18:53:36.00 33 02'00.00" 0.0
1475 7.49 18:33:47.66 46 13'09.02" 6.7
193 7.52 18:58:56.61 32 41'22.42" 3.2
585 7.73 19:16:22.10 38 08'01.46" 4.4
Press RETURN for #49 or enter CAT #:
The first column gives the catalog number for each star. The
stars on the list are displayed in order of increasing angular
separation (in degrees) from the requested coordinates, given in
the second column. Only stars with a declination within 10
degrees of that given will be displayed. The remaining columns
are the Right Ascension, Declination, and Magnitude. This display
was prepared using the standard catalog, ASTROCLK.CAT, which
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 103
includes the 109 Messier objects at the end of the file and have
magnitudes of 0.0. Note star #1593 in the sample above; this is a
Messier object rather than a true star. Note also that all
searches are made using the "raw" catalog data, in this case
J2000.0 Mean Place. The first 57 stars in ASTROCLK.CAT are the
standard USNO Navigational Stars, identical to the ASTROCLK
internal star database.
Press RETURN to select the first star in the list, #49
(Vega) in the sample, or enter the catalog number of another
star (which does not necessarily have to appear on the list). The
data for the selected star will be displayed in the Target
Tracking Display.
The message "SEARCHING ..." is displayed at the upper right
and the on-screen clocks are stopped during searchs. Once
started, a search may be cancelled by pressing SPACE BAR. When
the requested star has been selected, its catalog number
(prefixed by the letter "C" to indicate "Catalog") and all valid
names are displayed in the Tracking Display title, the star data
is read from the file, and the coordinates are displayed as with
internal star data. If a requested star cannot be found, ASTROCLK
displays a warning message; press RETURN to resume normal
operation.
For those interested in the technical details, ASTROCLK
expects the standard USNO ASCII catalog format of 96 characters
plus CR/LF per record as described in The Floppy Almanac User's
Guide, 2nd Edition, Appendix A. Provided the exact format is
maintained, the user may edit the catalog file or prepare a new
one. The following field definitions are extracted from that
appendix:
Field Field
Position Format Contents Units
----------------------------------------------------------------
1- 8 A8 Name1, left justified -----
9-16 A8 Name2, left justified -----
17-24 A8 Name3, left justified -----
25-38 F14.10 J2000.0 Right Ascension hours
39-52 F14.10 J2000.0 Declination degrees
53-62 F10.4 J2000.0 Proper Motion in RA sec/J Cent*
63-72 F10.4 J2000.0 Proper Motion in DEC arcsec/J Cent*
73-80 F8.4 Parallax arcsec
81-88 F8.4 Radial Velocity km/sec
89-96 F8.4 Visual Magnitude (or flux) mag, Jy
97-98 CR/LF Carriage Return + Line Feed
* Proper motion is given in seconds (RA) or arcseconds (DEC) per
Julian Century of 36525 days.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 104
PRECESSION AND STELLAR MOTION
The Earth's pole of rotation is tilted approximately 23
degrees 27 minutes from the plane of the ecliptic, that plane
which describes the Earth's orbit about the Sun. Rather than
constantly pointing to some fixed point in the heavens, however,
the gravitational influence of the Moon, Sun, and to a far lesser
extent the planets, cause the Earth to "wobble" slightly and the
pole describes a small circle with a period of about 25,770
years. This phenomena is known as lunisolar precession. A number
of other phenomena, such as nutation, also contribute to a lesser
extent to changes in the orientation of the Earth relative to the
plane of the ecliptic.
One of the by-products of precession is that Polaris, whose
proper name is Alpha Ursae Minoris, has not always been the pole
star. In ancient times Beta Ursae Minoris, (whose Arabic name
Kochab derives from the words "pole star", about 1,200 B.C.),
Alpha Draconis (about 3,000 B.C.) and Vega (about 13,000 B.C. and
again in about 13,000 A.D.) have been nearer to the true pole
than Polaris. Polaris will actually be closest to the true pole
in about the year 2,102 A.D. Some 25,000 years from now, Polaris
will again be the pole star as the cycle continues.
Another by-product of precession is that the standard
celestial coordinate system, using units of right ascension and
declination, changes gradually. The origin (0,0) of these
coordinates is the point on the ecliptic of the vernal equinox,
the intersection of the equator and the plane of the ecliptic.
This is commonly known as "The First Point of Aries", but over
the centuries since it acquired its name precession has caused it
to move out of that constellation and into the constellation
Pisces.
Time standards and terms of reference have also changed
considerably over the last fifty years adding to the possible
confusion. Better technology and demands for greater precision by
science and industry have been the driving causes. Over the past
decade or so new standards of time measurement and reference have
been adopted by the International Astronomical Union, the
governing body for all astronomical measurements.
Because of these changes and in order to provide a
consistent standard frame of reference, astronomers select an
"epoch", usually every 50 years, and base all of their
measurements against that standard point in time. Until recently,
the standard reference epoch has been 1950, now usually written
as B1950.0 (for Besselian epoch, another story related to the
time standard changes). Most references and publications have now
switched to the new standard epoch, J2000.0 (Julian epoch).
References requiring very high precision (such as the USNO
Almanacs) or calculated positions of the planets often use the
"equator and equinox of date", meaning the present epoch; in mid-
1988, for example, that is J1988.5.
When looking up the coordinates for a star or other object,
an astronomer must also note the epoch as well as the coordinates
themselves. If the epoch is different from that used for aligning
his instruments and/or is different from other objects to be
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 105
viewed, the data should be "precessed" or adjusted to account for
precession. The vernal equinox moves westward approximately 50
seconds of arc per year. The calculation of precession is
relatively complex and many writers choose to use an
approximation method which is sufficiently accurate only for
casual astronomical viewing or over very short time periods.
Unfortunately, a computer program such as ASTROCLK can be
used to cycle back and forth between epochs almost at will. The
"quick and dirty" approximations of the simpler methods can yield
cumulative errors that soon become unacceptable. A more rigorous
calculation for precession, the Improved IAU System, was adopted
in 1984; it is this method that is used in ASTROCLK. An earlier
method, developed in 1897 and published in 1906 by the American
astronomer Simon Newcomb, was used in earlier versions of
ASTROCLK and yielded comparable results. (Similar expressions
were published in Germany in 1830 by F. W. Bessel and
subsequently by others.) Although these calculations take
considerably more computer processing time, they produce errors
that are about two orders of magnitude less than typical
approximations. ASTROCLK also always resets the internal star
data to Epoch J2000.0 prior to precession calculations so as to
avoid cumulative errors. Since manually entered data cannot be
"reset"in this way, repetitive cycling from one epoch to another
will yield modest cumulative errors. The formulas employed are
described in the main text and the supplement of the 1984
Astronomical Almanac. When the internal data is precessed to
J1988.5, the results are in good agreement with USNO data for
that epoch given in Almanac for Computers 1988, pages E2 through
E10.
Further complicating the picture is the fact that the Earth
and the stars themselves are not stationary. The Earth's orbit
about the Sun causes parallax for nearby stars but the effect is
periodic and relatively small; it has been ignored for this
version of ASTROCLK. The changing position of the stars is known
as "proper motion". While stellar motion is extremely difficult
to measure for distant stars, proper motion data has been
collected on a large number of stars (including those used in
this program). ASTROCLK calculates the proper motion of stars
prior to calculating the effects of precession. The effects of
nutation and annual aberration are also included.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 106
DATES AND THE GREGORIAN CALENDAR
For convenience and standardization, many astronomical
calculations reference a unique point in time known as the
"Fundamental Epoch". This is defined as 12:00:00 at the Prime
Meridian (Greenwich) on 1 January, -4713 (often written as -4713
JAN 1.5). Note that the day starts at noon in conformance with
astronomical convention and corresponds to the time at which
accurate sun sights could be made. The time elapsed since then is
measured in units of days and the current date and time may thus
be expressed as a single number, UTC JULIAN DATE (usually known
simply as the Julian Date or JD). The number of days appears to
the left of the decimal point, and the time is represented by a
decimal fraction of a day. Years "before Christ" or "B.C." (but
not prior to 1 January 4713 B.C. for this program) are given as
negative numbers with no zero year. The Julian Date should not be
confused with the Day-of-the-Year, the number of days elapsed
during the current year, which is popularly and incorrectly also
sometimes referred to as the Julian Date.
However, astronomers delight (it would seem) in changing
their units of measure at depressingly frequent intervals;
multiple systems are sometimes in use simultaneously. Readers are
cautioned that some authors, especially in older works, include a
zero year in their calendars; using that scheme, 4713 B.C.
becomes year -4712. In the references I have used, for example,
Meeus prefers the zero year method while Duffet-Smith uses the
same method as ASTROCLK with no zero year; see BIBLIOGRAPHY for
references. I find the no zero year method far more convenient
and less confusing: years B.C have the same number and are simply
prefixed by a negative sign. Not all astronomers would agree.
To add to the potential confusion, prior to 1925 astronomers
considered that each calendar day commenced at NOON, agreeing
with the standard astronomical day numbering convention but in
conflict with civil practice. Modern astronomical convention,
however, begins the calendar day at MIDNIGHT, the same as the
civil calendar, and the practice is to apply the convention to
all dates -- even those prior to 1925. Care must therefore be
taken when interpreting older dates and times to ensure that the
date conventions employed are understood and converted if
necessary. This in addition to the various calendars in use! All
in all, a good argument for the use of Julian Dates which are
completely unambiguous -- if you ignore Julian Ephemeris Dates!
On an historical note, the Julian Date has been in use for
centuries by astronomers, geophysicists, chronologers, and others
who needed to have an unambiguous dating system based upon
continuing day counts. In fact, the the "Julian" part of Julian
Date has nothing to do with the Julian Calendar introduced by
Julius Caesar in 46 B.C. The Julian Date was so named by the
mathematician Scaliger when he introduced this method of day
counting in 1582, allegedly after his father, Julius. True or
not, the name has stayed with us regardless of its origins.
The starting date of January 1, -4713, for the Julian Date
was based upon the time it takes from one coincidence to the next
of a solar cycle (28 years), a lunar cycle (19 years), and the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 107
Roman Indiction (a Roman tax cycle of 15 years imposed by the
Emperor Diocletion during the period 284-305 A.D. and whose
connection to astronomy completely escapes me). However, the
product of those three cycle periods yields 7980 years, the
Julian Period. That period is of interest only with respect to
the selection of the starting time and date for the day counting
method, at which time all of the cycles, counted backwards, were
in coincidence. The real purpose of selecting such a date, of
course, was that it be distant enough in time that the resulting
day numbers would always be positive for events of interst.
Not too surprisingly, most historical dates were not
recorded using their Julian Date; for ancient dates, of course,
the Julian Calendar hadn't been invented yet, and for more recent
dates it was not (and still is not) in popular use. Enter the
calendar in all its varieties. Calendars have long been an
important part of almost every known civilization, especially
those dependent upon agriculture. Being able to predict the time
for planting and harvest was essential if the community was to
continue to have an adequate food supply. Stonehenge in England,
for example, is generally acknowledged to have been an
astronomical observatory of sorts, used to predict the equinoxes
and probably was also used for various religious and social
events as well. Except for the stones themselves and their
careful alignment, little else is known of the society they
represent. But, given the massive effort that was involved in its
construction, the importance of the calendar and the prediction
of the seasons to its builders is clear. The ancient Egyptians
watched Sirius (known to them as Sothis) for its appearance close
to the Sun in the morning sky, the First Heliacal Rising. This
marked the start of their 365 day calendar and coincided with the
rising of the Nile and the fertilizing of the Egyptian plain by
her waters. Almost without exception, every civilization of note
used a calendar, although their accuracy varied considerably.
The calendar having the most direct bearing on our present
system is the Roman Republican Calendar of ancient Rome and her
empire. Although the year started on the first of what is now
March (after Mars, the planet and also the God of War), the basic
structure of the calendar is quite similar to that in use today.
Its immediate successor, the Julian Calendar, came about as a
result of centuries of "adjustments" (more properly called
intercalation, the addition of extra days in the calendar) to
accommodate social, political, religious or other goals. Rulers
and court astronomers would insert or delete days seemingly
almost at random.
By the time of Julius Caesar, the Roman Republican Calendar
was more than two months out of synchronization with the seasons
and nothing was happening when it was supposed to. Spring was
occurring in winter months, winter in the fall, and so forth.
Caesar's Greek astronomer, Sosigenes, (inherited from Cleopatra
of Ptolemaic Egypt) figured out what should be done: a "final
adjustment" of 67 days would be made and the (then) last month of
the year, February, would be given an extra day every four years.
As a consequence, the year 46 B.C. became known as "The Year of
Confusion" and is the longest year on record, some 432 days.
Although the Julian Calendar was not consistently used for civil
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 108
purposes until 8 A.D., the need for a "standard" dating method
has led chronologers to extrapolate the Julian Calendar back in
time, calling it the Julian Proleptic Calendar to distinguish it
from other calendars in use.
Under the Julian Calendar, therefore, each year contained
365 days unless the year was divisible by four, in which case the
year contained 366 days. The additional day was inserted at the
end of February. The average length of the Julian year was thus
365.25 days. Given the relatively simple instruments and
mathematics of the time, the calendar that was devised then was
remarkably accurate and it continued in force until 1582.
Unfortunately, however, the tropical year (the time required
for the Earth to make one complete orbit around the sun and the
fundamental unit of our calendar) is actually 365.242199 days
rather than the 365.25 days used for the Julian Calendar. By 1582
that relatively small annual error, 0.007801 days or about 11
minutes 14 seconds, had accumulated and the calendar was again
out of step with the seasons, this time by some ten days.
Following a number of false starts by prior pontiffs, Pope
Gregory XIII ordered the use of an improved calendar, now known
as the Gregorian Calendar and in general civil use throughout
most of the world (sometimes in conjunction with an older,
religious calendar).
The new calendar directed that the dates 5 October through
14 October 1582 inclusive were to be abolished and that
henceforth all centennial years, years ending in "00", be leap
years only if divisible by 400. Therefore, 1700, 1800 and 1900
would NOT be Leap Years under the new calendar; 1600 and 2000
would still be Leap Years as before. Using the new Gregorian
method, 400 civil years contained 400 * 365 + 100 - 3 or 146097
days and the average length of the civil year was 365.2425 days
for a remaining error of approximately 0.0003 days. After all
that fuss and bother, the calendar is still some 26 seconds per
year too long, but it will take almost 3,000 more years, or until
about 4882 AD, for us to accumulate a one day error.
Some references (Encyclopaedia Britannica, for one) assert
that a further adjustment has been proposed to the Gregorian
Calendar: eliminate the Leap Year in years evenly divisible by
4000. This would reduce the error even further and it would be
some 20,000 years before a one day error would be accumulated!
Perhaps because the year 4000 A.D. is yet some time distant and
much may happen between then and now, most authors do not mention
or calculate the 4000 year adjustment. Given the lack of
unanimity in my sources, ASTROCLK also does not use the 4000 year
cycle in its calculation of future dates and the adjustment does
not apply to past dates.
The Gregorian Calendar, or the "New Style" as it was then
called, was of course immediately adopted by the catholic
countries: France, Portugal, Spain, and Italy as well as by
Denmark and the Netherlands. Catholic Scotland adopted it in 1600
but since England did not, this caused considerable confusion
between the two countries. The German Protestants waited 120
years or so, and it was not until 1752 that England and her
colonies finally adopted the new calendar. By then the error had
risen to 11 days (1700 was a Leap Year under the Julian Calendar
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 109
and was not under the Gregorian Calendar), and 3 September
through 13 September 1752 inclusive were abolished, accompanied
by much confusion and widespread disturbances. Even after formal
adoption of the new calendar, many English communities still
clung to the "Old Style" and the legend "O.S." may still be seen
on old tombstones. Following the French Revolution, France
abandoned the Gregorian Calendar for a new calendar beginning on
September 22, 1792; its use was short lived, however, and France
returned to the fold on January 1, 1806 and resumed use of the
Gregorian Calendar.
Good news travels slowly, it seems. Japan adopted the "new"
calendar in 1873 and China followed in 1911. But it wasn't until
the Bolsheviks came to power in 1917 and Pope Gregory had been
dead for more than 300 years that the Russians changed their
calendar. By then the error had further increased, to 13 days,
still the difference in 1988. (Halloween, October 31, 1988 is
October 18, 1988 using the Julian Calendar.) Not to be outdone by
the West, however, the Russians adopted the Greek Orthodox
calendar rule for a centennial year such that it is a leap year
only if, after dividing the year by 900, the remainder is either
200 or 600. The Soviet calendar is about five times more accurate
than the original Gregorian Calendar.
Because of all of this change and confusion, ASTROCLK simply
follows the original Gregorian Calendar as adopted in October of
1582 as the default calendar method. Dates prior to October of
1582 (and prior to 46 B.C. as well) are based upon the Julian
Calendar. However, as an option, ASTROCLK can use the British
date for the adoption of the Gregorian calendar in 1752, or it
can use the strict Julian calendar for all dates. Local dates in
other countries which did not immediately adopt the Gregorian
calendar must be adjusted for the period from October, 1582 (or
September, 1752 if that calendar is selected) through the date of
adoption. Dates for countries which use or used other calendars
are left as an exercise for the reader.
By setting ASTROCLK's internal CALENDAR FLAG (see SETTING
PROGRAM OPTIONS for details), dates may easily be converted
between the three calendar conventions. For example, select the
Perpetual Calendar (Display Mode 6), set the desired date (using
F3), then observe the date and calendar differences as you change
from one calendar convention to another (using ALT-F10). Because
ASTROCLK monitors the computer's internal clock (which includes
the current date), real time operation using the Julian Calendar
is not allowed; the situation is confusing enough without
ASTROCLK having to ignore part of the computer's time data.
Naturally, all three calendar conventions show the same date
prior to October of 1582; after September of 1752, both Gregorian
calendars are in synchronization and may be operated in real
time.
Quite oblivious to religion, politics and computers, the
Julian days have been spinning right along since 4713 B.C. They
have served their purpose well for astronomers and other
scientists. However, the true Julian Date (JD) is a rather large
number (4 February 1988 = 2447195.5) and the precision of some
calculators and micro-computer software is inadequate to the
task. Fortunately for those calculators and computers, the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 110
International Astronomical Union (IAU) at their Dublin meeting in
1955 adopted a special Dublin Julian Date (DJD) starting at noon
on January 0, 1900 or 1900 January 0.5 and which may be defined
as DJD=JD-2415020. The date can be confusing, however, since
there obviously is no 0th of January; the selected date is a
matter of astronomical convenience and actually is the same as
1899 December 31.5. The resulting number has only five digits to
the left of the decimal point (3 February 1988 = 32175.5). Both
methods, JD and DJD, are used internally by various ASTROCLK
routines. Note that the Julian Date cycles at noon rather than at
midnight as is the more usual practice for civil time; this can
easily cause confusion in calculations.
The Modified Julian Date (MJD) is a third method of
recording the Julian Date which also only requires five digits
(3 February 1988 = 47195.0) and is sufficient for most modern
purposes. Introduced in the late 1950's by space scientists, it
is defined as MJD=JD-2400000.5. An interesting side effect of
this purely mathematical definition is the rather unlikely
starting point of midnight (00:00:00 UT) on 17 November, 1858.
Like DJD above, this method reduces the precision required for
calculations but it also subtracts a half day so that the day
starts at midnight in conformance with civil time reckoning.
Although still mathematically accurate, MJD loses its advantage
of lower precision requirements if used prior to about 1600 A.D.
It is frequently used as a substitute for the true Julian Day by
many scientific organizations and publications. The MJD has been
sanctioned by various international commissions such as the
International Astronomical Union (IAU), the Consultative
Committee for Radio (CCIR), the advisory committee to the
International Telecommunications Union (ITU), and others who
recommend it as a decimal day count which is independent of the
civil calendar in use.
In addition to MJD, NASA also sometimes uses what they call
the Truncated Modified Julian Date or TJD; it is simply MJD less
the first digit, or TJD=JD-2440000.5. Like MJD, the day starts at
midnight rather than at noon (3 February 1988 = 7195.0). The
range of usefulness for TJD, based upon its having fewer digits,
is generally restricted to the current century. Mathematically,
of course, it is as accurate as any of the other methods.
Summarizing, the four standard methods of Julian day
counting in common use are:
00:00:00 UT
Name Starting Date 04 FEB 1988 Related to JD
---- ------------- ----------- -------------
JD -4713 JAN 1.5 2,447,195.5
MJD 1858 NOV 17.0 47,195.0 JD-2400000.5
DJD 1900 JAN 0.5 32,175.5 JD-2415020.0
TJD 1968 MAY 24.0 7,195.0 JD-2440000.5
The Julian Ephemeris Date (JED) is a slightly different
method of day counting based upon Ephemeris Time (ET, used pre-
1984) and Terrestrial Dynamical Time (TDT, used post-1983); JED
differs from the conventional Julian Date (JD) by a matter of
some seconds in this century (extrapolated to be 56.3 seconds in
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 111
1989, according to the Astronomical Almanac 1989). The actual
difference, called Delta T = ET/TDT-UT, is calculated well after
the fact using astronomical observations. For most astronomical
calculations, JED and JD may be used more or less interchangeably
unless high precision is required. However, for solar, lunar, and
planetary calculations, JED is usually required as an invariant
time system independent of the Earth's motion. Readers should use
care because many authors are somewhat casual on the subject and
may use the abbreviation "JD" to refer to either or both JD and
JED, and the correct usage may not be obvious.
The Julian Epoch (JE) and Besselian Epoch (BE) are two
additional astronomical dating methods, generally used when lower
precision is required or when the phenomenae of interest change
slowly with time; star catalogs and planetary tables are common
examples. The epoch dating methods are based upon the Julian
Century (36525 days) and the Tropical Century (36524.2199 days)
respectively. Texts written prior to about 1984 will write the
epoch without a prefix letter and the Besselian Epoch is assumed
(as in B1950.0). Again, however, recent authors often neglect to
add the prefix even when different epoch dating methods are
assumed; B1950.0 and J2000.0 are frequent examples. Most recent
star catalogs and publications reference astronomical data to the
current standard epoch, J2000.0. However, NASA and many planetary
tables and formulae still reference the prior standard epoch,
B1950.0, and some current data is referenced to the equinox of
date (or mid-year), such as J1988.5. Conversion is often required
in order that all data use the same reference epoch.
Last of all, Greenwich Sidereal Date (GSD) represents the
date using the sidereal day rather than the mean solar day. The
starting point for GSD is about 0.6 days earlier than JD but, due
to the shorter sidereal day, the date increases more rapidly than
JD; GSD is presently some 6700 days ahead of JD. I have not seen
it used in calculations, but the Astronomical Almanac includes
GSD in some of its tables.
The following list shows the value of these eight dating
methods at 00:00:00 UT on 04 FEB 1988:
JD 2447195.500000
MJD 47195.000000
DJD 32175.500000
TJD 7195.000000
JED 2447195.500649
JE J1988.091718
BE B1988.092741
GSD 2453896.370521
All of these dating methods are calculated by ASTROCLK and
used as required in its calculations. Display Mode 7, Julian Date
Information, displays this information except for GSD, which is
found using Display Mode 8, Precision Time Display #1.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 112
WHAT TIME IS IT?
This is a crucial question for astronomers and navigators
alike and is one of the reasons the two disciplines have been so
closely linked from time immemorial. Of course, both are
interested in the stars themselves, the first for scientific
reasons and the second for more practical purposes. From the
earliest recorded history, references are found to Polaris and
Kochab, each the pole star at different times, and the nearby Big
Dipper, two of whose stars serve as a "pointer" to Polaris. Their
principal use was as aids to navigation, both on land and on sea.
Not only does Polaris indicate true North with a fair degree of
accuracy, but its height above the horizon represents the
approximate latitude of the observer, the angle down from the
pole or up from the Equator.
So long as navigation was restricted to relatively confined
areas, such as the Mediterranean Sea, voyages stood a reasonably
good chance of reaching their intended destinations if the
navigator knew his direction and approximate speed. Polaris (and
later the magnetic compass, first described by an Englishman in
1180 but probably in use much earlier) could establish the
direction being traveled and the observation of speed, winds, and
tides could be combined with that direction to determine a ship's
probable course and position, a procedure known as "dead
reckoning". Elaborate charts covered with rhumb lines (lines
corresponding to various wind directions) were produced in the
13th century to aid the navigator in setting and plotting his
true course.
But as ships ventured further and further from known
landmarks, it became clear that this was not enough. Knowing only
their latitude (North-South position) and the direction of the
pole star, sailors found that they were often nowhere near their
destination. When sailing down the West coast of Africa, the
Portuguese, for example, adopted the practice of sailing South to
the desired latitude, then sailing East for however long it took
until they reached their destination. Columbus used this same
technique on his return trips to America. To further complicate
matters, the carefully drawn rhumb line charts assumed a flat
surface; the greater the distance traveled the greater the error
due to the fact that the Earth is a sphere and not a plane.
In an interesting footnote to history, the ancient Greeks
had concluded that the Earth was a sphere and described a more or
less circular orbit about the Sun -- or vice versa. Starting some
time around 450 B.C. give or take a few years and continuing for
more than 700 years, Greek astronomers proposed astronomical
theories and counter-theories culminating in Ptolemy's Almagest
in the middle of the second century AD. Erathosthenes (276-196
B.C.) made the first fairly accurate determination of the Earth's
diameter. He noticed that at Syene, Egypt (near present Aswan),
sunlight struck the bottom of a vertical well at noon. At the
same time and date in Alexandria, 5000 stadia north of Syene, he
noticed that the Sun's rays made an angle with the vertical of
about 1/50 of a circle (about 7 degrees). He therefore calculated
that the Earth's circumference must be 50 * 5000 or 250,000
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 113
stadia. Unfortunately, there were several stadia (the Greek unit
of length) in use and, depending upon which one you assume
Erasthones was using, his calculation could have been accurate to
within 1 percent or 20 percent too large.
Somewhere along the way this important bit of information,
the spherical Earth, was lost, misplaced or simply not believed
and by the middle ages many people in Europe were certain that
the Earth was flat. I'm not convinced that any of the great
navigators of the time were quite so naive and ill informed, but
maps drawn with that assumption in mind became less and less
accurate as voyages covered greater distances.
But the Earth, of course, really is a sphere (an oblate
spheroid, actually) and what was needed were maps based upon
latitude and longitude, not simply bearings. In 1569 Gerardus
Mercator published his world map based on a "true projection
suitable for navigation" and within a few decades navigators had
maps and tables which would permit the approximate determination
of position. The Mercator Projection is still used today for many
types of maps. Unfortunately, the maps of the day were not always
accurate, especially for unexplored areas of the globe, and even
when they were accurate everything depended upon being able to
estimate longitude as well as latitude.
The fifteenth and sixteenth centuries saw notable advances,
particularly in England, in the determination of longitude using
techniques such as lunar distances or the eclipses of the
satellites of Jupiter. The first astronomical ephemeris by
Regiomontanus was published in Nurnberg in 1474 and other
increasingly accurate ephemerides (tables of astronomical data)
useful to navigators were produced over the next two hundred
years. In 1675 the Royal Observatory was founded in Greenwich
with the specific object of providing the sailor with
astronomical data of the precision required for reliable
navigation.
Medieval astronomers knew that the time of a lunar eclipse
could be used to determine the local longitude, but that wasn't
very handy on a day to day basis. By the sixteenth century it was
also recognized that longitude could be determined by noting the
precise time and the position of the stars. Away from a stable
land platform and good instruments, however, knowing the time
accurately was all but impossible and time was a critical factor
in the longitude calculations. In 1714, following a series of
naval disasters caused by bad navigation, the English Parliament
established the Board of Longitude to address the problem. The
Board offered a prize of 20,000 pounds sterling, a princely sum
in those days, to anyone who could determine longitude to an
accuracy of thirty miles after a voyage of six weeks. An
Englishman by the name of John Harrison ultimately won the prize
on his fourth attempt using a marine chronometer fashioned in the
shape of a watch. And so began the practice of determining
position at sea by taking timed observations of the stars and
planets. The Royal Greenwich Observatory, situated on the Thames
River downstream from London, provided essential time services to
the Royal Navy and merchant seamen alike, and each captain would
carefully set his chronometer upon departure. Small wonder that
chronometer was among the most carefully guarded objects on board
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 114
ship, for their very lives might well depend upon its continuing
accuracy.
With little need for precision evident ashore, however,
local time was often a rather casual affair and based upon
apparent solar time, the time indicated by a sundial. Each town
or village would establish its own local time independent of its
neighbors. But apparent solar time is subject to considerable
variation as a result of the Earth's elliptical orbit and the
changes in the speed of rotation of the Earth. The difference
from day to day is relatively small, but the cumulative
difference can add up to about fifteen minutes over the course of
several months, a phenomena known as the Equation of Time. The
gradual improvement of clocks and watches during the seventeenth
century made these variations more obvious and forced the use of
mean solar time, apparent solar time averaged over a year, and
eventually caused the establishment of uniform time zones. The
railroads became prime movers in the push to standardize
timekeeping; schedules would be impossible to understand if every
stop used a different time convention. Most countries in Europe
therefore established single time zones using the time determined
at a single point such as Greenwich or Paris, but the United
States was forced by its size to adopt multiple time zones in
order to keep local times reasonable compared to the Sun. As
transportation and communication speeds continued to improve, the
various time zones were ultimately standardized in 1884 with
Greenwich selected as the Prime Meridian, and thus GMT or
Greenwich Mean Time became a worldwide standard. [However, until
1925, 0 hours GMT occured at noon rather than at midnight,
another source of possible confusion. The use of the designation
GMT has now been discontinued for the most part and replaced by
UTC, Coordinated Universal Time.]
The globe was marked with 24 standard meridians spaced at 15
degree (one hour) intervals and the meridian at 180 degrees was
designated the International Date Line. Most time zones are now
an integral number of hours different from Greenwich,
corresponding to the nearest standard meridian, and a few are at
a half hour multiples for local convenience (India, for example).
However, there still remain some odd zones here and there.
The accuracy and precision of our time measurements have
continued to improve as technology has advanced and in response
to the demands of the scientific and industrial community.
Traditionally, the fundamental unit of time measurement, the
second, was defined as 1/86,400 of a mean solar day. With the
improved accuracy of timekeeping came the need for a more
absolute standard and at the Dublin conference in 1955 the second
was redefined as 1/31,556,925.9747 of the tropical year as
measured on 1900 January 0.5, the same point selected for the
start of the Dublin Julian Date (DJD). This didn't last too long,
however, and in 1964 the International Committee on Weights and
Measures officially adopted the transition between two specific
energy levels of cesium-133 as the definition of the second with
the introduction of the atomic clock.
Timekeeping has now become internationally standardized and
the official custodian of the world's clocks is the Bureau
International de l'Heure (BIH) in Paris. Here in the United
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 115
States time standards and observation are the responsibility of
the National Bureau of Standards (NBS) and the U. S. Naval
Observatory (USNO). In 1965, after almost three hundred years as
the de facto time standard in the world, the Royal Greenwich
Observatory was restructured into more of a pure research
organization and has subsequently lost interest in, and ceased
most support for, time and time standards.
With the standardization and improved accuracy of our
timekeeping has come increased complexity. The old phrase
Greenwich Mean Time or GMT has now been officially discontinued
by most of the world, Great Britain and to a lesser extent the
United States (because of our close cooperation with Great
Britain on the Astronomical and Nautical Almanacs and related
works) being almost alone in continuing to use it, and then
primarily for navigators. Old habits die slowly, however, and
many people continue to use the old phrase, often unaware of the
change in name. GMT has generally been replaced by Coordinated
Universal Time, UTC, which is the time broadcast by the National
Bureau of Standards via WWV in Boulder, Colorado, and WWVH in
Honolulu, Hawaii, as well as other national radio time services.
For most purposes, those requiring accuracy to about one second,
GMT and UTC may be considered interchangeable. Individuals with a
military or aviation background will recognize ZULU Time, also
equivalent to Universal Coordinated Time.
For scientific work requiring high precision, however,
things are not nearly so simple. There are now four "standard"
Universal Times which take into account in varying degrees the
various phenomena that cause changes in time measurements over
long periods. In addition, a number of other time systems are
used including International Atomic Time (TAI) and Terrestrial
Dynamical Time (TDT). In 1984 TDT replaced Ephemeris Time (ET) as
the astronomical standard of time, the time system actually used
by most astronomers and computed well after the fact. UTC, tied
to the (irregular) rotation of the Earth, is currently "slow"
relative to TDT by slightly less than one minute; extrapolated
values given in the Astronomical Almanac 1989, Page K9, are 55.8
seconds for 1988 and 56.3 seconds for 1989. For the present, all
calculations within ASTROCLK assume UT1 and ignore differences
with other UT time standards.
The following simplified definitions describe the various
time standards in general use at the present time, or which have
been in common use during this century.
A.1 U.S. Naval Observatory Atomic Time, used from January
1, 1958 through December 31, 1971. ET = A.1 + 32.15
seconds. Replaced by TAI (qv) on January 1, 1972.
ET Ephemeris Time, replaced in 1984 by Terrestrial
Dynamical Time (qv).
GAST Greenwich Apparent Sidereal Time. Greenwich Hour Angle
of the true equinox of date.
GMST Greenwich Mean Sidereal Time. Greenwich Hour Angle of
the mean equinox of date.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 116
GMT Greenwich Mean Time, a term now used almost exclusively
in the United Kingdom and for navigation. Most modern
references now use UT1 (qv) instead. Prior to 1925, 0
hours GMT occured at noon rather than at midnight; care
must be used when referencing older documents to take
this change into account.
TAI International Atomic Time. The unit of TAI time is the
SI (Systeme International) second. This time standard
is based upon the analysis of the atomic time standards
of many countries and is related to the radiation of
Cesium 133. "Atomic time, in the general relativistic
sense, probably keeps the proper time of a moving
observer in a gravitational field." [Taff, p 102, see
BIBLIOGRAPHY.] TAI was adopted as a standard on January
1, 1972, replacing A.1 (USNO Atomic Time) which was
used from January 1, 1958.
TDT Terrestrial Dynamical Time, used for astronomical
ephemerides for observations from the surface of the
Earth. TDT/ET = TAI + 32.184 seconds. For most
purposes, ET (up to 1983 December 31) and TDT (from
1984 January 1) can be regarded as a continuous time
scale. In 1989, TDT is ahead of UT by approximately
56.3 seconds; the difference is 56.7 seconds for 1990.
TDB Barycentric Dynamical Time, used for high precision
astronomical ephemerides referred to the barycenter
(center of mass) of the solar system. TDB never varies
from TDT by more than 1.7 milliseconds and is not used
by ASTROCLK. TDB was previously known as Coordinate
Time.
UT0 Classical universal time, based upon the mathematical
relationship between mean solar time and mean sidereal
time. Not directly used or calculated in ASTROCLK.
UT1 UT0 corrected for precession, the polar motion of the
Earth. This slow wobbling motion describes a circle
about 30 feet in radius over a period of approximately
25,800 years. The combined gravitational fields of the
Sun and Moon acting upon the non-spherical Earth cause
the direction of the Earth's rotation axis to gyrate
slowly. UT1 is now the official designation for, and is
the same as, Greenwich Mean Time, GMT. In program
ASTROCLK, the abbreviation UT is used to mean UT1 and
is used for all calculations and displays unless
specifically noted otherwise. Except in the Precision
Time Displays, ASTROCLK ignores the difference between
UT1 and UTC, considering them identical.
UT2 UT1 corrected for a slight (maximum seasonal difference
of approximately 0.035 second) periodic variation in
the speed of rotation of the Earth caused by the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 117
varying distances and relative directions of the Sun
and Moon which in turn continuously alter the strength
and direction of the gravitational field. Not used or
calculated in ASTROCLK.
UTC Coordinated Universal Time. UTC was originally a
smoothed version of UT2 (pre-1972) and is now based
directly upon TAI. On January 1, 1972 the difference
between TAI and UTC was exactly 10 seconds. Since that
date, adjustments of exactly one second are made as
required on June 30th or December 31st in order to keep
UTC and UT1 within 0.9 seconds of each other. When a
change is required, the last minute of those months
will have 59 or 61 seconds. UTC is the basis for most
radio time services (including WWV/WWVH) and our civil
and legal time systems. It is also, of course, the time
signal most of us use to synchronize time-dependent
equipment and (directly or indirectly) to set our
clocks. As noted above, ASTROCLK generally assumes
UT1=UTC unless noted otherwise; the difference is less
than the setting/running errors of the average micro-
computer system clock.
ZULU A distinctive phonetic acronym having no particular
meaning. ZULU time is equivalent to UTC and is used in
commercial avaition and by the U. S. military services
in order to avoid confusion over local time zones.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 118
PRECISION AND ACCURACY TESTS
A number of tests have been performed to examine the
precision and/or accuracy of various calculations made by
ASTROCLK. The principal data used for testing and comparison are
derived from: Astronomical Almanac 1988 and 1989 (both usually
refered to as AA, unless a more specific reference is required),
USNO Almanac for Computers, 1988 (AFC88); USNO Floppy Almanac
1988 and 1989 (FA generally, or FA88 and FA89 if required);
USNO Interactive Computer Ephemeris (ICE); Astronomical Formulae
for Calculators (AFC); and, Astronomy with Your Personal Computer
(AYPC). See BIBLIOGRAPHY for the full references. Unless noted
otherwise, all tests and comparisons were made using a Zenith Z-
248 computer (IBM PC/AT compatible with 80286 processor) equipped
with an 80287 math coprocessor. Representative tests were
repeated on a Zenith Z-183 laptop (IBM PC/XT compatible with
80C88 processor) with or without a math coprocessor with no
differences observed other than execution speed.
Strict mathematicians and scientists may complain about the
precision to which data is typically displayed by ASTROCLK. The
reader is reminded at various points in this text that the
displayed precision may exceed the accuracy of the data, a
practice which is definitely frowned upon in scientific circles,
but I plead special circumstances for ASTROCLK.
First and foremost, ASTROCLK has been developed over a
considerable period of time, and the process still continues. The
accuracy of all data have been consistently improved over that
time, and many items have gradually been improved to the point
where the accuracy and the displayed precision are roughly the
same -- the desired objective. In some cases, stellar Apparent
Geocentric Equatorial Coordinates for example, the improvement
has reached the limits of the QuickBASIC compiler and the
accuracy is essentially equal to the best available sources.
Second, many different items are displayed using the same
units and in multiple formats but having different or unknown
accuracy; it is convenient from a programming standpoint to use
common subroutines for display purposes. Attempting to tailor
the display each of the dozens of quantities calculated by
ASTROCLK to the probably accuracy is impractical.
Finally, even in cases where the accuracy is known to be
lower than the displayed precision, trends and relative
magnitudes of change can be observed and are reasonably accurate;
these second order effects are of some interest to me (and
perhaps others), and would be lost if the data were truncated to
the known accuracy.
COMPILER
Microsoft QuickBASIC, Version 4.50, is the language used for
ASTROCLK. Code may be executed in a quasi-interpretive mode or it
may be compiled to an executable file. Two different Microsoft
programs, QB and BC, are used for the two methods respectively.
The distribution version of ASTROCLK is the compiled version of
the code. When required for precision, the double-precision
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 119
floating point format has been used for numeric data; this eight
byte format has a precision of 15 or 16 digits and an approximate
magnitude range of from 4.9E-324 to 1.8E+308. [As of Version
8903, the program could still be compiled with QuickBASIC Version
4.00b, but that compatibility may not be maintained and will not
be tested for future ASTROCLK versions.]
Unfortunately, testing (and confidence) is complicated by
the fact that the interpreted version appears to be very
sensitive to the order of evaluation and/or to mixing variable
types within an expression. For example, using Version 4.00
(since updated to Version 4.50), typical calculated results for
mean sidereal time varied by plus or minus 0.000011 hours simply
by changing the type of variables. Compiled results were the same
for all calculations tested, regardless of type or order, and
have been used for all comparisons with other data. In spite of
the interpreter situation, however, I have concluded that the
flexibility and ease of use of QuickBASIC outweighs concern over
its problems. In any event, the accuracy and precision seem
sufficient for the intended use in ASTROCLK.
CALENDAR DATES
The calendar algorithms used are either modeled upon those
given in AFC and AYPC or have been developed specifically for
ASTROCLK. The calendar displays for October, 1582 and September,
1752 use special algorithms to allow for the 10 or 11 missing
days. The default ASTROCLK calendar strictly follows the Julian
Calendar from its adoption in 46 B.C. through the Gregorian
Calendar at its adoption in 1582. Alternatively, the user may
select the strict Julian Calendar for ALL dates, or select the
British date of adpotion of the Gregorian Calendar in 1752. See
the section SETTING PROGRAM OPTIONS for additional details. Dates
prior to 46 B.C. are merely an extension of the Julian Calendar
back into time, known as the Julian Proleptic Calendar, and
bear no particular relationship to calendar(s) in actual use. For
times subsequent to 46 B.C., extensive tests have disclosed no
errors. Dates for countries adopting the Gregorian Calendar
subsequent to October, 1582 or September, 1752 must be adjusted
manually. The intercalation proposed and/or adopted for 4000 A.D.
and thereafter on a 4000 year cycle has not been included.
As a matter of personal preference and in company with some
(but not all!) of my references, I have adopted a year numbering
scheme which includes no zero year. Readers should note that
other authors prefer year numbering WITH a zero year, and
feelings seem to run high on the subject. Mathematically, of
course, any continuous set of numbers must include zero. However,
common usage does not include a zero year. The confusion and
errors which may result from converting common years such as 4713
B.C. into year number -4712 seem too high a price to pay to
maintain conformance with the mathematical niceties. Since
opinion and practice in the astronomical community is divided
anyway, the reader must always check negative dates to determine
the year numbering system being used by a given author.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 120
JULIAN DATES
Julian Dates have been compared with various Astronomical
Almanacs and other sources and are exact. The algorithm used is
modeled upon that given in AFC. The Julian Date calculations
should be accurate from -4713 onward. Note that ASTROCLK uses a
year numbering scheme with no year zero (see above); other
authors prefer a scheme with a zero year. The day count is also
presented in three other formats: MJD, DJD, and TJD. See the
section JULIAN DATES AND THE GREGORIAN CALENDAR for additional
discussion.
UNIVERSAL TIMES
Coordinated Universal Time (UTC), the time broadcast by
WWV/WWVH and others, is not the same as Universal Time (UT=UT1)
but the difference is maintained at less than 0.9 seconds and for
most purposes this difference can be ignored. ASTROCLK assumes UT
for all time and date calculations and displays with one
exception: the Precision Time Display. In this case, the correct
UTC time is calculated and displayed to full accuracy for the
period 1972 through 1989 when data from AA, Pages K8 and K9, may
be applied. Outside this time period, I have made more or less
arbitrary assumptions to supply missing data. AA does not include
data for Delta UT = UT-UTC; the following tabulation was made
using ASTROCLK data for 00:00:00.00 UT and the UT date shown.
1988 DELTA UT = UT - UTC (seconds)
----------------------------------
JAN 1 +0.18 JUL 1 -0.06
FEB 1 +0.14 AUG 1 -0.11
MAR 1 +0.10 SEP 1 -0.15
APR 1 +0.06 OCT 1 -0.19
MAY 1 +0.02 NOV 1 -0.23
JUN 1 -0.02 DEC 1 -0.27
TERRESTRIAL DYNAMICAL TIME
Delta T, defined as TDT/ET - UT, is determined retro-
spectively approximately one year after the fact. Since most
planetary phenomena require the use of TDT/ET but ASTROCLK is
based upon UT, Delta T is required to relate the two time scales.
Data for reduction of UT versus TDT (Terrestrial Dynamical
Time) times are given in AA, Pages K8 and K9, annually for the
period 1620 through 1987 with extrapolated data for 1988 through
1990. ASTROCLK uses the published values for Delta T as of
0h UT January 1 each year for the available interval. For
simplicity, I have assumed that Delta T varies linearly from
datum to datum; interpolation would probably yield more accurate
results, but the difference would not be significant for most of
ASTROCLK's calculations. Prior to 1984, the designation changes
to Ephemeris Time (ET). The two time scales are considered
continuous by ASTROCLK.
Data for the future behaviour of the rotation of the Earth
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 121
is, of course, mostly well-informed speculation. However, it
determines how Universal Time will change with respect to
Terrestrial Dynamical Time and, in the context of ASTROCLK, is
required for planetary positions especially. Similarly, while the
data for the last several hundred years can at least be inferred
from historical records with some degree of confidence, little or
no accurate information exists for ancient times. A number of
formulae have been published which allow the estimation of Delta
T over extended periods.
Versions of ASTROCLK prior to 8848 calculated Delta T using
a formula by Meeus (AFC); Version 8848 changes to a formula by
Morrison and Stephenson (1982) and used by Bretagnon and Simon
(1986). [See BIBLIOGRAPHY for reference.] The two methods produce
values of Delta T that differ by about three hours at 4000 BC,
out of approximately thirty hours. I have no particular reason to
believe one formula more accurate than the other, but I switched
to Bretagnon and Simon because their planetary position formulae
are widely recognized as some of the more accurate which are
suitable for micro-computers. Their planetary data, therefore,
form a useful basis for comparison with ASTROCLK's planetary
position calculations at any instant in time; using the same time
scales makes this comparison far simpler. However, TDT or ET
should be used with caution outside the period 1620 through 1990.
INTERNATIONAL ATOMIC TIME (TAI)
Data for reduction of TAI versus UTC times (Delta AT) is
given in AA, Page K9, annually for the period January, 1972
through July, 1985. I do not recall any subsequent Leap Seconds
until December 31, 1987 and have therefore increased Delta AT to
+24 on January 1, 1988. Prior to its adoption as a standard in
1972, TAI is replaced by USNO A.1 (see below). Subsequent to
1988, I have arbitrarily adjusted TAI by inserting one or more
Leap Seconds so that the difference between UT and UTC is always
less than one second. The difference between TAI and TDT/ET is
32.184 seconds. TAI should be used with caution outside the
period January 1972 through December 1988.
USNO ATOMIC TIME (A.1)
Prior to the adoption of International Atomic Time, the U.S.
Naval Observatory maintained its own atomic time standard, known
as A.1. On January 1, 1958, the difference between A.1 and UTC
was exactly zero seconds. By January 1, 1972 (when TAI was
adopted), the difference was ten seconds. In calculating Delta AT
for A.1, I have assumed a linear rate of change and that
adjustments are made on June 30th or December 31st as appropriate
to maintain the proper relationship with UT. The difference
between A.1 and ET is 32.15 seconds.
SIDEREAL TIMES
Greenwich mean and apparent sidereal times at 00:00:00 UT
for each day of the year are given in AA, pages B8 through B15;
selected dates are also given in AFC88, page A3, or they may be
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 122
computed for any time using FA. ASTROCLK computed Greenwich Mean
Sidereal Times are exact compared to AA and FA88 using the
Precision Time Display #1, Display Mode 8. The displayed values
for Greenwich Apparent Sidereal Times have a lower accuracy (due
to the complex calculations required to compute nutation and the
Equation of the Equinoxes); the accuracy is substantially better
than 0.01 seconds.
A comparison using FA88 for 1 January at 0h UT and 12h UT at
each of the decades 1950 through 1990 showed GMST to be exact at
the displayed precision of 0.0001 seconds for all samples, and
GAST to have an average error of -0.0007 seconds and maximum
errors of +0.0013 and -0.0025 seconds. The GAST average error
works out to about 1/100,000,000 (10E-8). LMST is GMST adjusted
for the local longitude and is therefore as accurate as the
longitude data. LAST also depends upon longitude; using the same
longitude for ASTROCLK and FA88, comparison of LAST showed
results comparable to GAST.
The algorithms for time calculations in general and for
the sidereal time calculations in particular were revised and
refined at Version 8826 and again at Version 8831, with an
improvement in accuracy of at least an order of magnitude. The
Precision Time Displays were also added at Version 8826. [Thanks
to Ward Harman for detecting an error at other than 0h UT.] If
you wish to calculate the data shown in AA, switch to the
Precision Time Display #1. Display Mode 8, and enter the time and
date in UT using Function Key F3 as follows (April 1988 is used
as an example):
0U (time: 00:00:00 UT)
1,4,1988 (date: APR 1, 1988)
Use Function Key F7 to select the desired data format.
PRECESSION
Precessing the preset internal star database, derived from
USNO FA88 data, from J2000.0 to J1988.5 yields coordinates in
good agreement with USNO Almanac for Computers 1988 to the
precision given there, although the accuracy decreases slightly
for declinations nearer the poles. Beginning with Version 8905,
the precession method was changed from Newcomb (B1900.0) to
Improved IAU System (J2000.0) as described in the main text and
the supplement to the 1984 Astronomical Almanac. The resulting
precessed data are little changed.
Representative test results are shown below. Prior to
precessing any star in the internal star database, ASTROCLK
automatically restores all data to J2000.0 in order to eliminate
cumulative errors. Proper motion for objects entered manually may
also be entered, or set to zero if not known; tracking data which
is precessed over long periods of time when proper motion
parameters are set to zero should be used with caution. Solar
system objects should always be entered with proper motion
parameters set to zero.
Care should be taken when manually entering data to ensure
that the data epoch is the same as that of the internal database.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 123
In order to maintain consistent data within ASTROCLK, the
internal star database should first be precessed to a data epoch,
then manual data referenced to that epoch should be entered.
After that, all data may be precessed to the final epoch; using
this procedure, both the manually entered data as well as the
internal data will all refer to the same epoch.
SAMPLE PRECESSION DATA FOR J1988.5
AFC88 ASTROCLK
# Star Name SHA/DEC SHA/DEC
----------------------------------------------
0 Polaris 325.0618 325.064979
89.2126 89.212613
10 Aldebaran 291.1851 291.185085
16.4868 16.486829
20 Procyon 245.3249 245.324922
5.2551 5.255091
30 ACrux 173.5116 173.512040
-63.0354 -63.035405
40 Kochab 137.3174 137.317359
74.2025 74.202525
50 Nunki 76.3618 76.361780
-26.3118 -26.311751
The data from AFC88 (Almanac for Computers 1988) is given
there for Mean Place (J1988.5) as shown. The data from
ASTROCLK has been precessed from J2000.0 to J1988.5 using
Function Key F8. Note slightly degraded accuracy near the
North and South poles.
SHA: Sidereal Hour Angle in degrees, first line. SHA is
related to Right Ascension (in hours) by the formula
SHA=360-RA*15. The data format shown for ASTROCLK is
obtained using Function Key ALT-F7 (for SHA) and Function
Key F7 (for degrees and decimal fractions of a degree).
DEC: Declination in degrees, second line. The data format
shown for ASTROCLK is obtained using Function Key F7 (for
degrees and decimal fractions of a degree).
A similar comparison with the Astronomical Almanac 1989,
Appendix H ("Bright Stars, J1989.5"), yields accuracies of 0.1
seconds in Right Ascension and 1 second of arc in Declination
when the ASTROCLK data are rounded to the same precision as that
given in the Astronomical Almanac.
In its discussion of rigorous precession, the Astronomical
Almanac 1989 includes an example of the reduction of celestial
coordinates for a fictitious star on page B40. The time is given
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 124
as 0h TDT 1989 JAN 1. Entering the relevant example data
(including proper motion, but not parallax or velocity) into
ASTROCLK yields the following data:
EQUATORIAL COORDINATES [J2000.0]:
RIGHT ASCENSION (hours): 14:39:36.09
DECLINATION (degrees): -60 50'07.13"
APPARENT COORDINATES [J1989.0]:
RIGHT ASCENSION (hours): 14:38:49.34
DECLINATION (degrees): -60 47'17.56"
The J2000.0 Equatorial Coordinates shown above are the mean data
at the standard epoch, essentially identical to those entered
from the Astronomical Almanac. The Right Ascension is correct
when the data is rounded to the precision shown; the Declination
is low by 0.01 arcseconds and results from internal rounding
and/or precision errors. The computed J1989.0 Apparent Geocentric
Equatorial Coordinates given in the Astronomical Almanac are:
RIGHT ASCENSION (hours): 14:38:49.394
DECLINATION (degrees): -60 47'17.49"
Even without the inclusion of velocity factors, the results from
ASTROCLK agree with the Astronomical Almanac to -0.05 seconds in
Right Ascension and +0.07 seconds in Declination. These errors
approach the limits imposed by the double precision floating
point representation of numbers within QuickBASIC and probably
represent the best accuracy attainable in this context.
Beginning with Version 8903, the internal or external
catalog value for the visual magnitude of the selected star or
object is displayed at the lower right of the window border in
the Tracking Display, Display Mode 0.
SOLAR POSITION CALCULATIONS
The computation of the position of the Sun is crucial to
many of ASTROCLK's other calculations. I have selected the
Apparent Geocentric Coordinates as representative of the accuracy
of the calculated solar position; these values are more or less
"at the end of the line" in the series of solar calculations and
therefore should provide a good basis for comparision with other
sources as well as implying the accuracy of prior calculations.
In the table which follows, the data source is noted in the
right hand column: AA is the Astronomical Almanac, 1988, Pages C4
through C18; FA is the USNO Floppy Almanac, 1988, Version 2.11.88
with time and date set automatically from ASTROCLK using ALT-F9;
and, AC is ASTROCLK, Version 8903, Precision Data Display #2. All
data are for 0 hours TDT.
Use Function Key F3 and enter "0T" to set TDT time in order
to obtain the same ASTROCLK results for a given date. Note that
the date displayed by ASTROCLK is UTC DATE, which differs from
the TDT DATE by some +56 seconds in 1988; the UTC DATE will
therefore show as the prior day for all months and the prior year
for January 1.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 125
Use Function Key F3 and enter "0U" to set UT time in order
to obtain the same Floppy Almanac results for a given date. Note
that ASTROCLK writes the UT time to the file FA.DFT but the
Floppy Almanac assumes the time as TDT for Apparent Geocentric
Positions calculations. [Other Floppy Almanac calculations
correctly interpret the time from FA.DFT as UT.]
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 126
1988 APPARENT GEOCENTRIC COORDINATES OF THE SUN
@ 0h TDT
Right Ascen Declination Distance
HH MM SS.SS DD MM SS.SS (AU)
-----------------------------------------------------------------
JAN 1 18 42 32.35 -23 04 58.0 0.9832806 AA
32.351 57.98 0.9832806 FA
32.09 59.13 0.98328271 AC
FEB 1 20 55 10.26 -17 22 51.2 0.9852225 AA
10.263 51.19 0.9852225 FA
10.10 52.74 0.98522551 AC
MAR 1 22 48 28.17 -7 35 04.3 0.9908696 AA
28.166 04.27 0.9908696 FA
28.10 05.36 0.99087354 AC
APR 1 0 42 13.66 4 32 33.1 0.9993011 AA
13.657 33.09 0.9993011 FA
13.57 32.50 0.99930318 AC
MAY 1 2 33 39.46 15 04 46.1 1.0076058 AA
39.462 46.07 1.0076058 FA
39.27 45.59 1.00760326 AC
JUN 1 4 36 31.28 22 03 24.4 1.0140599 AA
31.285 24.39 1.0140599 FA
30.97 24.52 1.01405250 AC
JUL 1 6 40 49.08 23 06 40.5 1.0166665 AA
49.076 40.53 1.0166665 FA
48.79 41.54 1.01665800 AC
AUG 1 8 45 34.69 18 01 10.9 1.0149312 AA
34.695 10.93 1.0149312 FA
34.61 11.55 1.01492350 AC
SEP 1 10 41 32.50 8 16 56.4 1.0091422 AA
32.500 56.39 1.0091422 FA
32.68 54.99 1.00913318 AC
OCT 1 12 29 29.89 -3 11 08.2 1.0010858 AA
29.888 08.23 1.0010858 FA
30.28 11.19 1.00107716 AC
NOV 1 14 25 35.77 -14 25 48.7 0.9924284 AA
35.772 48.75 0.9924284 FA
36.18 51.13 0.99242345 AC
DEC 1 16 29 14.33 -21 48 17.1 0.9860075 AA
14.332 17.11 0.9860075 FA
14.59 17.81 0.98600708 AC
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 127
MAJOR PLANET POSITION CALCULATIONS
Care must be taken when comparing ASTROCLK's planetary data
with other sources to ensure that the data are calculated for the
same time, date, and epoch. No extensive accuracy comparisons
have yet been performed for ASTROCLK's planetary position
calculations, but spot checks against the Astronomical Almanac,
USNO Floppy Almanac, Bretagnon and Simon, Sky & Telescope
Magazine, and Astronomy Magazine indicate good agreement.
As compared against the monthly magazine positions, ASTROCLK
provides essentially the same data, and can generate the data for
any date rather than for selected dates within a month. In
general, predicted errors for the algorithms used by ASTROCLK are
on the order of 10" for the calculated positions, and typical
errors for a small number of samples have been of that order of
magnitude as compared against the USNO Floppy Almanac. The
position of Pluto is calculated using osculating elements as of
1988 JAN 1, and the errors will increase as the time difference
from that date becomes greater.
The Astronomical Almanac 1988 includes Geocentric Distance
and Coordinates for the planets. The coordinates for Venus are
given on pages E18 through E21. The data are given at 0h TDT for
each day of 1988. Entering 0h TDT 1988 DEC 25 into ASTROCLK and
selecting Venus yields the following data:
Heliocentric Longitude: 214 52'30.43"
Heliocentric Latitude: 2 15'35.90"
Heliocentric Radius (AU): 0.722754
Appar Geocentric Longitude: 249 03'00.77"
Appar Geocentric Latitude: 1 05'37.50"
Geocentric Distance (AU): 1.4936045 <===
Apparent Right Ascen [J1988.9]: 16:30:05.90 <===
Apparent Declination [J1988.9]: -20 43'44.27" <===
Apparent Right Ascen [J2000.0]: 16:30:44.93
Apparent Declination [J2000.0]: -20 45'08.39"
Angular Size (arcsec): 11.33
The True Geocentric Distance and Apparent Equatorial Coordinates
given in the Astronomical Almanac for that date are:
GEOCENTRIC DISTANCE (AU): 1.4935568
RIGHT ASCENSION (hours): 16:30:05.982
DECLINATION (degrees): -20 43'44.04"
The data compare extremely well. The ASTROCLK errors are
+0.0000477 AU in Geocentric Distance, -0.082 seconds in Right
Ascension, and +0.24 arcseconds in Declination.
Beginning with Version 8903, the approximate visual
magnitude of the selected planet is also displayed on the
Tracking Display, Display Mode 0, at the lower right of the
window border.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 128
MINOR PLANET POSITION CALCULATIONS
It is difficult to directly compare minor planet data from
the available sources. ASTROCLK computes all minor planet data in
the same way as for major planets: apparent position as of the
ecliptic and equinox of date. The Astronomical Almanac gives
geocentric positions as Astrometric J2000.0 Right Ascension and
Declination, and other sources use B1950.0. However, data for the
major planets are available as of the ecliptic and equinox of
date; using the osculating elements given in the Astronomical
Almanac for the major planets and processing these data through
ASTROCLK's minor planet software yields position data generally
accurate to a second or arcsecond at or very near the date of
osculation. This is better accuracy than ASTROCLK's internal
major planet data and algorithms usually provide. I have
interpreted these results to mean that my methodology is
essentially accurate and correct.
For example, using the minor planet catalog PLANETS.MPC
(which contains osculating elements @ 1989 MAR 15.0 for the eight
major planets from the Astronomical Almanac 1989), the following
heliocentric and geocentric results were obtained:
HELIOCENTRIC POSITION FOR MERCURY @ 1989 MAR 15.0
Longitude Latitude Radius Vec Source
--------------------------------------------------
243 44 08.0 -6 22 52.2 0.4440226 AA 1989
243 44 07.53 -6 22 52.25 0.4440219 ASTROCLK
GEOCENTRIC POSITION FOR MERCURY @ 1989 MAR 15.0
Rt. Ascension Declination Delta Source
--------------------------------------------------
22 37 19.211 -11 05 56.36 1.2713558 AA 1989
22 37 19.52 -11 05 55.27 1.2713511 ASTROCLK
CELESTIAL NAVIGATION CALCULATIONS
ASTROCLK's celestial navigation calculations are adapted
from the material presented in the Nautical Almanac 1989, pages
277 and following. ASTROCLK was tested by using the Nautical
Almanac data adjusted to offset ASTROCLK's automatic internal
refraction calculations, the same practice used by the Nautical
Almanac. These data therefore represent the result when extremely
precise altitude measurements have been taken and when the
atmospheric refraction, horizon dip, course, and speed are
precisely known. In practice, altitude measurements to this
precision are all but impossible outside an observatory, and
atmospheric refraction can seldom be predicted to an accuracy of
much better than approximately 0.5 minutes of arc.
Under these circumstances and using the example data on page
282 of the Nautical Almanac 1989, ASTROCLK calculates the
position of a moving ship to an accuracy of 0.03 nautical miles
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 129
(0.05 kilometers or less than 200 feet) as compared to the
results calculated in the Nautical Almanac. This level of
accuracy is unlikely to be achieved in actual use. In addition to
the potential errors mentioned in the previous paragraph, note in
particular that ASTROCLK assumes UTC = UT (or that the computer
is set to UT rather than UTC); if UTC is used, the resulting time
difference (0.9 seconds maximum) can introduce an error in
longitude as much as plus or minus 0.2'.
The example in the text only shows that ASTROCLK will
produce essentially the same result as the Nautical Almanac. The
Nautical Almanac does not give the "correct" position for the
example data nor does it characterize the errors to be expected
using its method. By testing ASTROCLK against itself, we can
measure the inherent accuracy of the calculations in another way.
Setting the time to 05:00UT on 11 November 1989, the local
coordinates to the preset location "CAL", and using the Target
Tracking Display to make our three "star sights", the following
data are obtained:
Star Ho Hc Hc'
-----------------------------------------------------
12 Capella 36 22 03.11 36 20 46.88 36 20 46.93
49 Vega 25 44 32.72 25 42 36.22 25 42 36.38
51 Altair 23 23 04.13 23 20 54.20 23 20 54.40
Ho is the Apparent Altitude displayed by ASTROCLK and used as the
Altitude input for star sights, Hc is the calculated Altitude
displayed by ASTROCLK, and Hc' is the calculated Altitude derived
from the Apparent Altitude and displayed with the navigation
results. This incidentally shows that the internal refraction
calculation is reversible. The results obtained are:
Actual Calculated
---------------------------------
-120 34 00.00 -120 34 15.96
38 09 00.00 38 09 00.63
The calculated position is 0.27 nm (0.49 km) from the actual
position, a very respectable result but somewhat different from
the comparison with the Nautical Almanac example. It is probably
more representative of the accuracy of the celestial navigation
calculations.
The determination of position by dead reckoning is dependent
only upon the accuracy of the initial position and the course and
speed parameters. No attempt has been made to compensate for
other factors such as wind and/or current; ASTROCLK assumes that
the course and speed data have already been corrected for those
factors as required.
Determining the current position using ASTROCLK's celestial
and dead reckoning navigation functions requires that the
procedures given in the text be followed carefully and that
accurate position fixes or star sights be used. Users should take
note that the celestial navigation portion of ASTROCLK can be
very sensitive to input data errors and should therefore use
these functions with care.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 130
J2000.0 INTERNAL STAR DATABASE
Versions of ASTROCLK prior to 8811 used star data manually
entered from SKY CATALOGUE 2000.0 (Sky Publishing, 1982). The
current star data was extracted from FA88 Version 2.11.88 (star
catalog file STAR1.CAT dated 03-02-87) and was substituted in
Version 8811 and following. The visual magnitudes for each star
were manually added at Version 8903. This substitution was more a
matter of personal preference and judgment than the result of any
explicit information regarding the inherent accuracy of one
source over the other. Be that as it may, my reasons were: a more
recent publication date; FA88 data are used for scientific and
navigational purposes and I have therefore assumed higher
accuracy for the stars selected by USNO; FA88 data are given to
higher precision; and, finally, the data were transferred to
ASTROCLK directly. A secondary reason for the use of the FA88
data is that the AFC88 data for J1988.5 presumably uses the same
USNO master data base as FA88 and therefore provides a useful
basis for the comparison of ASTROCLK's internal precession
calculations (see PRECESSION above for representative results).
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 131
ASTROCLK MESSAGES AND ERRORS
Program ASTROCLK generally tries to detect or work around
anticipated error conditions which might interfere with program
operation. Most non-critical error conditions or warning messages
are displayed in the ASTROCLK error window at the lower left of
the screen; these conditions usually do not prevent normal
program operation (although the operation causing the error may
not be performed). Warning messages are displayed with a BROWN
(or YELLOW, depending upon your color monitor) background and
the word "CAUTION" appearing in the window title; error messages
are displayed with a RED background and the word "ERROR"
appearing in the window title. Monochrome monitors, of course,
won't display in color! The ASTROCLK error number appears in the
lower right of the window border. After you understand the
message, press RETURN to resume program execution. Other
corrective action may be indicated in the message description
below.
However, certain error conditions may not be detected or
processed within ASTROCLK, and may cause QuickBASIC or DOS error
messages to be displayed or may cause the program to fail to
operate as expected; typical such messages or conditions (shown
in parentheses) are described at the end of this section. When
such an error is detected, an error message is displayed giving
the QuickBASIC error number and error message (if available, see
Page 410 of the QuickBASIC 4.50 Reference Manual for a list of
the normal error messages). Press RETURN and ASTROCLK is aborted
and the user is returned to DOS.
ASTROCLK Numbered Errors and Cautions:
--------------------------------------
[01] CAUTION: ASTROCLK is not
accurate before -4713!
The date has been set prior to the year -4713 using
Function Key F3. Many of ASTROCLK's date and time algorithms
either fail or are inaccurate prior to -4713. You should use
Function Key F3 to set a legal date. If the one of the
Julian Date or Epoch formats was used for date input, the
date is set to JD 0.000000 rather than the date entered;
otherwise, the date is left as entered. Execution is allowed
to continue after pressing RETURN.
[02] Illegal Longitude!
-180 <= Longitude <= 180
[03] Illegal Latitude!
-90 <= Latitude <= 90
An illegal value was entered for the Longitude or
Latitude when setting new local coordinates with F6. The
Longitude must be between -180 degrees (west) and 180
degrees (east); the Latitude must be greater than or equal
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 132
to -90 degrees (south) and less than or equal to 90 degrees
(north). Re-enter the correct value.
[04] Illegal Rt. Ascension!
0 <= RtAscen < 24
[05] Illegal Declination!
-90 <= Decln <= 90
An illegal value was entered for the Right Ascension or
Declination when setting target coordinates with F5. The
Right Ascension must be greater than or equal to zero hours
and less than 24 hours; the Declination must be greater than
or equal to -90 degrees (south) and less than or equal to 90
(north) degrees. Re-enter the correct value.
[06] Illegal Altitude!
-90 <= Altitude <= 90
[07] Illegal Azimuth!
0 <= Azimuth <360
An illegal value was entered for the Visual Altitude or
Visual Azimuth when setting the visual coordinates with F5.
The Visual Altitude must be greater than or equal to -90
degrees and less than or equal to 90 degrees; the Visual
Azimuth must be greater than or equal to zero degrees and
less than 360 degrees. Re-enter the correct value.
[10] Catalog file not found!
(Check with ALT-F10)
A search of the external star catalog was requested
with F5 and the external catalog could not be found. Use
ALT-F10 to set the correct file name and/or path.
[11] External Catalog Search
cancelled by operator!
While searching the external star catalog, the operator
pressed the ESC key and cancelled the search. The current
data are left unchanged.
[12] Requested star Name/Number
not found. Try again!
While searching the external star catalog for a
specified star name or star number, the requested item could
not be found in the catalog. Verify the name or number and
try again.
[13] City file not found!
(Check with ALT-F10)
A search of the external file of city names was
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 133
requested with F6 and the file could not be found. Use ALT-
F10 to set the correct file name and/or path.
[14] Requested city not found
in current city file!
A search of the external file of city names was
requested with F6 and the specified city or abbreviation
could not be found in the file. Verify that the correct city
file is being used. Check the city name or verify the city
file with a text editor to see if the city is included.
[22] Check PATH; should include
the backslash char (\)!
ASTROCLK has detected that the default path or the path
just entered does not include the backslash character. The
backslash character should normally be the first character
of any path so that the path may be properly found. Repeat
the path selection process from the start to correct the
incorrect path(s). See the section SETTING PROGRAM OPTIONS
for additional information. This is a CAUTION message; press
RETURN to resume ASTROCLK operation.
[23] Check ASTROCLK path; add a
drive specification!
ASTROCLK detected a drive specification (such as "D:")
in the path for the Floppy Almanac but not in the path for
ASTROCLK. If the path for the Floppy Almanac includes a
drive then the path for ASTROCLK must also include a drive.
For example, if the Floppy Almanac path is "D:\FA", then the
ASTROCLK path should have the form "C:\ASTROCLK". If the
drive is the same for both paths, do not include the drive
in either path, e.g. "\FA" and "\ASTROCLK". If you do not
intend to use the Floppy Almanac, enter SPACE to clear the
Floppy Almanac path. Repeat the path selection process from
the start to correct the incorrect path(s). See the section
SETTING PROGRAM OPTIONS for additional information. This is
a CAUTION message; press RETURN to resume ASTROCLK
operation.
[24] Illegal DATE requested!
Check CALENDAR FLAG
You have requested an illegal date which falls either
in October, 1582 (Calendar Flag = 1) or September, 1752
(Calendar Flag = 2) and which was one of the dates abolished
as part of the adoption of the Gregorian Calendar. Observe
the calendar for the month in question using Display Mode 6
to see the days that were deleted. Check the CALENDAR FLAG
using ALT-F10.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 134
[25] Illegal DATE requested!
Req. year NOT Leap Year!
You have requested February 29th for a year which is
not a Leap Year for the calendar convention currently in use
by ASTROCLK. Verify the requested date and check the
CALENDAR FLAG using ALT-F10.
[26] Illegal DATE requested!
Illegal MONTH and/or DAY!
You have requested an illegal MONTH and/or an illegal
DAY. The MONTH must be from 1 to 12, and the DAY must be
from 0 to the maximum number of days in the MONTH. Day 0 is
allowed to conform with astronomical usage. Separate each
item with a comma: dd[.d],mm,yyyy.
[27] Clocks must be SIMULATED/
OFF with Julian Calendar!
You have requested the strict Julian Calendar using
ALT-F10 while the clocks are ON. The clocks are set OFF;
ASTROCLK cannot operate in real time with the Julian
Calendar. You may, however, enable SIMULATION using ALT-F4
to observe time/date changes with the Julian Calendar.
[28] CALENDAR FLAG restored to
1 = Gregorian @ 1582!
After setting the CALENDAR FLAG for the strict Julian
Calendar, you have pressed F4 to restart ASTROCLK's clocks.
The clocks will be set ON, but the date and time will be
restored to system time and the Calendar Flag set for the
Gregorian Calendar as of October, 1582. ASTROCLK cannot
operate in real time with the Julian Calendar. However, you
may use ALT-F4 for simulated real time with the Julian
Calendar.
[30] Illegal PLANET name or
number requested!
You must enter either a valid number (1,2,4-9) or at
least the first letter of the planet's name. Mercury and
Mars require at least two letters, "ME" and "MA"
respectively. The Earth is planet number 3, and planetary
data are not calculated. Press RETURN and enter a valid
number or name.
[31] Requested Minor Planet
NUMBER not in file!
You have requested a Minor Planet number which is not
included in the current Minor Planet Catalog. The range of
available minor planets is shown in the upper portion of the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 135
window.
[32] <mpfilename>:
File not found!
The Minor Planet Catalog whose path and name is shown
on the first line of the error message could not be
found. Check that the path and name have been correctly
entered using ALT-F10.
[33] <mpfilename> is
not BINARY or is CORRUPT!
The Minor Planet Catalog whose path and name is shown
on the first line of the error message is not a BINARY
catalog OR its contents are corrupt. Check that the path and
name have been correctly entered using ALT-F10.
[34] Requested Minor Planet
NAME not found!
The requested minor planet NAME could not be matched in
the current Minor Planet Catalog. The name either does not
exist in the catalog or you have misspelled it. Names may be
entered in upper or lower case and only sufficient letters
are required to unambiguously identify the desired minor
planet(s). Do not include a trailing space in the name.
[35] Data for this Minor Planet
is MISSING from Catalog!
Although the requested Minor Planet Number is within
the range of this catalog, the catalog has no data for this
Minor Planet. (A blank record is included.)
[40] Old version ASTROCLK.INI!
File read and deleted.
ASTROCLK has read file ASTROCLK.INI and it was not in
the current version's format. The file was read up to the
point where an error was detected and then the file was
deleted. For most prior versions of ASTROCLK, all of the
local coordinate and time zone information will have been
read correctly; to be sure, verify this information on the
screen and correct any items in error. Upon exit, ASTROCLK
will write a new copy of ASTROCLK.INI in the correct format.
[41] Can't delete ASTROCLK.INI!
Disk write-protected/R.O.?
ASTROCLK attempted to delete an old version of the file
ASTROCLK.INI and the delete failed. This message will
immediately follow error message #22 above. The disk may be
write protected or full. ASTROCLK attempts to update the
file ASTROCLK.INI each time the program completes and the
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 136
program expects that the disk drive will NOT be write
protected. The file may be set to "Read Only" which also
prevents the delete and update functions. The program will
operate properly but local coordinates and other program
parameters cannot be saved from one execution to the next.
"Error writing ASTROCLK.INI" will also probably occur when
you exit ASTROCLK.
[50] ICE and FA are disabled!
Use ALT-F10 to enable.
You have used ALT-F9 to request the ICE or FA and both
programs are disabled. Use ALT-F10 to enable one or the
other and to set the proper drive and/or path.
[51] Cannot run Floppy Almanac:
File FA.DFT open error!
[52] Cannot run ICE Ephemeris:
File ICE.DFT open error!
You have used ALT-F9 to request the ICE or FA and
ASTROCLK is unable to open the file ICE.DFT/FA.DFT to write
the current default parameter information. Check the ICE/FA
and ASTROCLK paths using ALT-F10. Alternatively, your disk
may be full. Press RETURN to resume ASTROCLK operation.
[53] Cannot run Floppy Almanac:
1988 <= Year <= 1999
ASTROCLK's date is set prior to 15 DEC 1987 or after
15 JAN 2000 and you have used ALT-F9 to request the Floppy
Almanac. If you have a version of the Floppy Almanac which
will execute outside those dates, you must exit ASTROCLK
using F9 and run it manually. Alternatively, change to ICE
for dates from 1800 through 2049. ASTROCLK resumes normal
operation after pressing RETURN.
[54] Cannot run ICE Ephemeris:
1800 <= Year <= 2049
ASTROCLK's date is set prior to 1800 or after 2049 and
you have used ALT-F9 to request the ICE. ICE actually will
only execute for dates from December 21, 1800 through June
7, 2049. ASTROCLK resumes normal operation after pressing
RETURN.
[60] NAVIGATION mode disabled;
Set with F10 [F10 + F2].
The navigation made is currently disabled. Use Function
Keys F10 + F10 to set the UT ZONE OFFSET, then use Function
Keys F10 + F2 to set the navigation data. ASTROCLK resumes
normal operation after pressing RETURN.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 137
[61] Must set UT ZONE OFFSET
TIME using F10 + F10!
This function cannot be performed until you set the UT
ZONE OFFSET using Function Keys F10 + F10. ASTROCLK resumes
normal operation after pressing RETURN.
[62] Invalid Navigation Data!
Must set using F10 + F2.
The navigation data is not valid or has been disabled
by the use of Function Key F6. Use Function Keys F10 + F2 to
re-enable existing data or enter new data. ASTROCLK resumes
normal operation after pressing RETURN.
[63] Invalid Navigation Data!
Requires 2 Star Sights."
ASTROCLK requires a minimum of 2 star sights in order
to calculate the position. Data for Star #1 is required, and
data must be entered for either Star #2 or Star #3 or both.
ASTROCLK resumes normal operation after pressing RETURN.
[99] QuickBASIC 4.50 ERR = nn
<error description>
An error has been detected by QuickBASIC during
execution of ASTROCLK. "nn" is the QuickBASIC Run-Time Error
Code, as described in Table D-1, Page 476, of the QB4
Language Reference Manual. <error description> is the plain
text description of the detected error. After RETURN is
pressed, execution of program ASTROCLK is aborted and the
user is returned to the DOS prompt. NOTE: All expected
errors have been trapped by other error routines, as
described above. If you receive this error message, please
report the circumstances to Dave Ransom either by mail or to
the BBS at (231) 541-7299.
Other ASTROCLK, QuickBASIC and DOS Errors:
------------------------------------------
Error writing ASTROCLK.INI
This error message occurs as you exit ASTROCLK and may
indicate that your disk is full or write protected. The disk
drive used for ASTROCLK must NOT be write protected since
updated information is written to the disk upon exit. The
error may also be related to a change in ASTROCLK version,
or the file may have been manually edited and the format
changed. ASTROCLK terminates but ASTROCLK.INI may not be
updated to reflect current data.
To correct the problem, delete file ASTROCLK.INI. The
next time you use ASTROCLK, the default coordinates (Rancho
Palos Verdes, CA) will appear; use Function Key F6 to re-
enter your local coordinates.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 138
(DOS SHELL fails to execute)
No error message is displayed but when Function Key F9
is pressed ASTROCLK pauses momentarily and then continues
normal execution without displaying the DOS prompt. Either
insufficient memory is available to execute COMMAND.COM or
COMMAND.COM cannot be located. If present, remove any RAM
DISK from your CONFIG.SYS file and do not execute any large
Terminate and Stay Resident (TSR) programs when using
ASTROCLK. See your DOS documentation for use of the SET
command to verify the COMSPEC parameter (which gives the
location of COMMAND.COM).
(ALT-F3 fails to set software clock)
The message "Bad command ..." may be seen briefly at
the lower left of the screen. Verify that your version of
DOS provides the program RTCLOCK to set the software clock
from the hardware clock AND that the program can be found
using the current DOS path. If you are using a batch file
called RTCLOCK.BAT to set your clock, verify its operation
and that it can be found using the current DOS path. See
also the section PROGRAM OPERATION for further information.
(SHIFT-F3 fails to set alarm time, alarm sounds immediately)
The alarm must be set using LOCAL TIME and the selected
time may not be more than 23 hours in the future. If the
alarm time would have occurred within the past hour, the
alarm will immediately sound and the alarm window at the
lower right will appear then immediately disappear.
(ALT-F9 fails to execute the USNO Floppy Almanac or ICE)
Insufficient memory may be available to execute the
Floppy Almanac or ICE. See "DOS SHELL fails to execute"
above. The version of FA required for the current date may
not be present: a different version of FA is required for
each calendar year named "FA88.EXE" for 1988, "FA89.EXE" for
1989, and so forth.
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 139
A BRIEF EDITORIAL
One of the first decisions that has to be made when writing
software is the choice of programming language. Of course, for
the individual who only wishes to use the end product and doesn't
care how it was done, it couldn't make less difference as long as
the software gets the job done. Each programming language has
its strong points and its weaknesses, and personal preference
usually plays a strong role in the choices that are made. For
ASTROCLK, my choice is Microsoft's QuickBASIC.
I've written software professionally for many years using
quite a few different computers and languages and have frequently
encountered the attitude that "BASIC isn't real programming, it's
just a hobby." The people who feel that way should really check
out Microsoft's QuickBASIC, Version 4.50, before they are helped
off their soapbox. BASIC has undergone a major evolution in the
past several years. While it may not be suited to every job, the
times that a BASIC programmer must resort to assembly language or
some other higher level language are diminishing at an extremely
rapid rate. It has been a real pleasure for me to rediscover
BASIC and I use it frequently. Unlike "C", for example, BASIC is
a language that I can be away from for an extended time and not
have to start all over when I resume using it. For the other side
of the coin, however, see also the COMPILER discussion under
PRECISION AND ACCURACY TESTS.
There is another factor that strongly influenced my decision
to use QuickBASIC to implement ASTROCLK. As has been written
elsewhere, BASIC in one form or another is the "lingua franca" of
micro-computers. If my efforts are to be instructive or useful to
the greatest number of interested computer users and would-be
programmers, they must be understandable to the majority of those
individuals. Writing in C or Fortran may result in "better" code,
but I would cut myself off from too many people who are not
familiar with those programming languages. BASIC, and Microsoft's
QuickBASIC in particular, is relatively easy to understand and
the software product is easily obtained, well documented and
inexpensive.
One of the items on my list of pet peeves is "shareware" or
"userware", as it is commonly called. While I don't begrudge an
author the opportunity to recoup some of his or her investment in
a program, I am not completely convinced that our free bulletin
board systems are an appropriate marketplace. But even if they
are, some authors go far beyond a simple request for a modest
donation if you like and use their software. Threats of legal
action annoy me almost as much as "free" programs that are
crippled unless and until you send in money; given the quality of
some of this software, any amount sometimes seems exorbitant. I'd
rather use supported commercial software that performs as
advertised right out of the box. I hope the individuals who
practice these threats and deceptions quietly starve; in the mean
time, they are embarrassing honest folk everywhere.
What ever happened to "freeware"? It's now rare indeed to
find software that is really free, and even more rare to find the
source for that software. And the source can be a terrific
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 140
learning tool for the interested programmer and hobbyist alike.
Maybe I just remember the days of CP/M too well, when you didn't
consider (or trust) public software unless the source was
available. You didn't get many unpleasant surprises when someone
was willing to sign his name and show you how it was done. I owe
a considerable debt to those authors who provided their source in
the past. Perhaps the recent outbreak of so-called computer
viruses will encourage more users to demand, and authors to
include, the source for their programs. I certainly hope so!
My thanks to Dave Evers of Quincy, Illinois, for his public
domain WINDOW TOOLS, a version of which was adapted for use in
ASTROCLK. While it wouldn't have been that difficult to write the
simple window routines I needed, it was nice to have some
QuickBASIC routines already debugged, documented, and which
included the source code.
A project like ASTROCLK can continue indefinitely; so far,
it's been going on for over two years. Being considered for
future versions are Lunar tracking data, times for rising and
setting, and various other items large and small that may or may
not ever happen. Portions of code to implement new features may
appear from time to time in ASTROCLK and are either not used or
are commented out. As new or improved features are contemplated,
I try to strike a balance between accuracy and reasonable
computational times -- a battle I seem destined to lose one way
or the other. Already, a math coprocessor is the only way to keep
all operations in strict real time when the clocks are running
and you wish to view planetary data.
Program ASTROCLK is free for non-commercial use. Use it if
you like it, discard it if you don't. There are no warranties of
any kind. Version 8806 was the first public release of ASTROCLK in
February of 1988. While I don't know of any obvious or
catastrophic bugs after many versions, updates, and corrections,
I will probably never feel sufficiently confident to say there
aren't any. Microsoft's QuickBASIC 4.50 IS NOT included and IS
required to compile the source files. The compiled version,
ASTROCLK.EXE, is a stand-alone program and does not require
QuickBASIC support.
Comments and suggestions are welcome, and any error or bug
reports will be greatly appreciated. Use the mail or call the
bulletin board system (BBS) at the number below and leave a
message for "SYSOP" or "Dave Ransom". The BBS has an automatic
power controller; if it doesn't answer by the third ring, hang
up, and then call back in TWO MINUTES. (It's an older computer,
and those two minutes are used for boot-up and BBS housekeeping
chores.) The BBS will always have the most recent version of
ASTROCLK in compressed format; ASTROCLK is located in the
ASTRONOMY area, File Area #5. Updated versions are posted at
irregular intervals, typically every four to eight weeks. Use
program PAK, Version 2.10 or higher (also available on the
BBS), to decompress the files.
(213) 541-7299 [24 hours, 2400/1200 baud]
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 141
The BBS version of ASTROCLK is available in three compressed
files (currently approaching a total of about 500K), and download
times are considerable. Individuals without access to a modem or
who wish to avoid toll charges for these large files may obtain a
complete set of ASTROCLK disks with the current version (MS-DOS
DS/DD, specify 5-1/4" 360K or 3-1/2" 720K) by sending US $20.00
to cover disks, postage and handling.
David H. Ransom, Jr.
7130 Avenida Altisima
Rancho Palos Verdes, CA 90274
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 142
BIBLIOGRAPHY
The following principal sources have been consulted during
the preparation and/or testing of Program ASTROCLK and this text.
------, THE ASTRONOMICAL ALMANAC 1984. U. S. Government Printing
Office, Washington, DC, 1983.
------, THE ASTRONOMICAL ALMANAC 1988. U. S. Government Printing
Office, Washington, DC, 1987.
------, THE ASTRONOMICAL ALMANAC 1989. U. S. Government Printing
Office, Washington, DC, 1988.
------, THE ASTRONOMICAL ALMANAC 1990. U. S. Government Printing
Office, Washington, DC, 1989.
------, THE NAUTICAL ALMANAC 1989. U. S. Government Printing
Office, Washington, DC, 1987.
------, NBS TIME & FREQUENCY DISSEMINATION SERVICES, NBS Special
Publication 432. U. S. Government Printing Office, Washington,
DC, 1979.
Acker, Agnes and Jaschek, Carlos, ASTRONOMICAL METHODS AND
CALCULATIONS. John Wiley & Sons, New York, NY, 1986.
[First published in French in 1981.]
Bretagnon, Pierre and Simon, Jean-Louis, PLANETARY TABLES AND
PROGRAMS FROM -4000 TO +2800. Willmann-Bell, Inc., Richmond, VA,
1986.
Burgess, Eric, CELESTIAL BASIC. Sybex Inc., Berkeley, CA, 1982
Carroll, Tim S., THE FLOPPY ALMANAC USER'S GUIDE, 2nd Edition.
Nautical Almanac Office, United States Naval Observatory,
Washington, DC, 1988.
Danby, J. M. A., FUNDAMENTALS OF CELESTIAL MECHANICS, 2nd
Edition. Willmann-Bell, Inc., Richmond, VA, 1988.
Doggett, LeRoy E. et al, ALMANAC FOR COMPUTERS 1988. Nautical
Almanac Office, United States Naval Observatory, Washington, DC,
1988.
Duffett-Smith, Peter, ASTRONOMY WITH YOUR PERSONAL COMPUTER.
Cambridge University Press, New York, NY, Reprinted (with
corrections) 1986.
[NOTE: The disk available from Cambridge University Press,
containing the programs from this text, does NOT include the
1986 corrections (as of mid-1988). In particular, subroutine
PELEMENT, Page 141, contains errors in the DATA statements
for Mercury and Mars, lines 3725 and 3800; see text for
ASTROCLK Astronomical Clock and Celestial Tracking Program Page 143
corrections.]
Duffett-Smith, Peter, PRACTICAL ASTRONOMY WITH YOUR CALCULATOR,
2nd Edition. Cambridge University Press, New York, NY, 1981.
Espenshade, Edward B., Jr., Editor, GOODE'S WORLD ATLAS, 17th
Edition. Rand McNally & Co., Chicago, IL, 1987.
Hirshfeld, Alan and Sinnot, Roger W., Editors, SKY CATALOGUE
2000.0. Sky Publishing Corp., Cambridge, MA, 1982.
Hobbs, Richard R., MARINE NAVIGATION 2, 2nd Edition. Naval
Institude Press, Anapolis, MD, 1987.
Lawrence, J. L., BASIC ASTRONOMY WITH A PC. Willmann-Bell, Inc.,
Richmond, VA, 1989.
[NOTE: A diskette is also available with the BASIC programs
for IBM-compatible PC's.]
Meeus, Jean, ASTRONOMICAL FORMULAE FOR CALCULATORS, 4th Edition.
Willmann-Bell, Inc., Richmond, VA, 1988.
[NOTE: The 4th Edition is identical to the 3rd Edition with
the exception of an added Chapter 43 giving formulae for the
position of Pluto.]
Menzel, Donald H. and Pasachoff, Jay M., A FIELD GUIDE TO THE
STARS AND PLANETS, 2nd Edition. Houghton Mifflin Co., Boston,
MA, 1983.
Sinnott, Roger W., monthly column "Astronomical Computing", Sky &
Telescope Magazine, various issues 1984 through 1989.
Taff, Laurence G., CELESTIAL MECHANICS. John Wiley & Sons, New
York, NY, 1985.