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? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? PURE MATH CONNECTORS ?
????????????????????????
Terms Nx, Egs, and Ess, can be shown to be mathematically
connected by direct steps which bypass the physical dynamic
terms. This does not mean the physical dynamic terms do not
exist, it only means that it is possible to quickly work back
and forth between Ess, Egs, and Nx, when a few connector rules
are known. These rules include the following:
Given an Nx term:
then: Egs = ?(1 - 1/Nx)
and: Nx = root 1/(1 - (Egs)?)
and: Ess = root 1 - (Egs)?
and: Ess = ?(1/Nx) = 1/?Nx
These connector rules can be more readily shown in a table,
as follows:
TABLE 8
??????????????????????????????????????????????????????????????
? FOR EXAMPLE, GIVEN THAT Nx = ?3 = 1.732050807 ?
??????????????????????????????????????????????????????????????
? ?
? Then: for GRAVITY relativity ?
? ?
? ???????????????? ?
? ? 1 ?
? 1. Egs = ? 1 - ??? = .650115167 ?
? \? ?3 ?
? ?
? ?
? 1 ?
? So that: Nx = ??????????? = 1.732050807 ?
? 1 - (Egs)? ?
? ?
??????????????????????????????????????????????????????????????
Cont.
??????????????????????????????????????????????????????????????
? ?
? Then: for SPECIAL relativity ?
? ?
? ?????????? ?
? ? 1 ?
? 2. Ess = ? ???? = .759835685 ?
? \? ?3 ?
? ?
??????????????????????????????????????????????????????????????
? ?
? ?????????????? ?
? ? 2G M ?
? Ess = ? ?????? = .759835685 ?
? \? C? R ?
? ?
? ?
? 2G M ?
? And: Ess? = ?????? = .577350269 ?
? C? R ?
??????????????????????????????????????????????????????????????
Cont.
??????????????????????????????????????????????????????????????
? ?
? Ess? C? R ?
? So that: M = ??????????? ?
? 2G ?
? ?
? ????????????? ?
? And: Ess = \? 1 - (Egs)? = .759835685 ?
? ?
? ?????????????? ?
? And: Egs = \? 1 - (Ess)? = .650115167 ?
? ?
? 1 ?
? And: Ess = ????? = .759835685 ?
? ?Nx ?
? ?
? 1 ?
? So that: Nx = ??????? = 1.732050807 ?
? (Ess)? ?
? ?
? And: Vx = C / 1/Egs = Velocity ?
? ?
??????????????????????????????????????????????????????????????
??????????????????????????????????????????????????????????????
? ?
? NOTE: There are specific similar distinctions ?
? between the Nx terms for the two relativities, ?
? and first given Egs and Ess terms, shown in ?
? TABLE 8 as 1, and 2. ?
? ?
??????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????
? ?
? These above shown pure math permutations are ?
? true when given any value for Nx, or Egs, or Ess. ?
? ?
? With these rules it is possible to freely move back ?
? and forth to arrive at key terms for gravitational ?
? and special relativites. ?
? ?
? For instance, given a special effect (Ess) for a ?
? body moving at a high velocity, then equivalent ?
? gravitational effect (Egs) in relativity is directly ?
? known by a single step calculation, for instance ?
? by: ?
? ?
? ?????????????? ?
? Egs = \? 1 - (Ess)? ?
? ?
? And what portion the given moving body's mass ?
? is to a black hole silent partner equivalent, ?
? is directly known by a single step calculation, ?
? for instance by: ?
? ?
? 1 ?
? Nx = ?????? because: Nx = Mbh/M ?
? (Ess)? ?
? ?
????????????????????????????????????????????????????????????
When dealing with real events which occur at the critical
mass limit Mc, where then Mbh/Mc = GH (the Golden Harmonic
Ratio 1.618034), then pure math connectors can appear slightly
confusing, in that certain pure math factors exactly occur through
functions of the Golden Ratio, rather than through relativistic
field dynamics.
For instance:
TABLE 9
????????????????????????????????????????????????????????????
? GIVEN THAT Nx = 1.61803398875 = The Golden Ratio ?
????????????????????????????????????????????????????????????
? Then also: ?
? ?
? Egs = 1/GH = GH - 1 = .6180339 ?
? ?
? ??????????????? ?
? And: Egs = \? 1 - (Ess)? = .6180339 ?
? ?
? ?
? And: Nx = Egs + 1 = 1.6180339 ?
? ?
????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????
? ?
? And: Ess = ?Egs = .7861514 ?
? ?
? And: Nx = (Ess x 1/Egs)? = 1.6180339 ?
? ?
? And: Nx = Ess? + 1 = 1.6180339 ?
? ?
? Etcetera ?
? ?
? ?
? BUT THESE ARE TRUE ONLY WHEN NX = THE GOLDEN RATIO ?
? ?
????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? WHY Egs AND Ess ARE INTRINSICALLY RELATED ?
?????????????????????????????????????????????
In a closer look at the preceding, some
further facets are learned. In particular:
EQUATION Z-18
For example: Taking data for Ess and Egs from EQ Z-17-3 ;
and: M+ from table 6
then: in EQ Z-18 ;
?????????????????
Ess = \? 1 - (Egs)?
where: M+ = ?Nx ; when: Nx = Mbh
??? ???
M M
and so: in EQ Z-18-1 ;
EQUATION Z-18-1
?????????????????????
Ess of .003161416 = \? 1 - (.999995002)?
because: (M+/M) = ?Nx
as when: in EQ Z-18-2 ;
EQUATION Z-18-2
(1.482558107 x 10 to 36 grms)
??????????????????????????????? = 316. 313878376 = ?100054.469653
(4.686984066 x 10 to 33 grms)
where: ?100054.469653 = ?Nx x 100,000
because: Nx is ratio 1.000544617404
and: Mbh / 1.000544617404 gave Mass1 for our study model
and: Mass1 / 100,000 gave Mass2 for our study model
NOTE: The true value of ?(Nx x 100,000) = 316.313865868 =
?100054.4617404, is slightly departed from the actual Nx
value for Mass2 shown immediately above. The departure
is due to intrinsic truncation in accuracy, where a few
digits are clipped from the tail end of the HIGH special
relativity Ess term .003161416, and the LOW Egs term
.999995002.
?????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????????????????
? ????????????????????? SPECIFIC CONCLUSIONS ????????????????????? ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
It is now clear, according to the above derivations which begin
with EQ T and continue through EQ Z-18-2, that a fundamental
barrier exists in physics, which limits special relativistic
effects on a visible moving mass entity to a pre-determinant
black hole gravitational mass equivalent, gained by a
pre-determinant limit in velocity.
The pre-determination on the entity is as seen by a stationary
observer watching the mass entity move at relativistic velocities.
At its pre-determinant limit in velocity, the mass entity
transfigures into a black hole and disappears from view.
(This does not mean that the black hole cannot keep acceler-
ating. What it means is that the possibility of such further
acceleration is not addressed in any way, in the scope of this
disclosure. This exploration ends with the original radius R
transfigured into an event horizon R- = R'. And so as an event
horizon radius R- will thereafter behave in dissimilar ways
than in the physical form of a radius R. Such dissimilarity
in behavior of radii is discussed further above at the start
of Part 2, as Items 1 and 1A under: 'A Comparison Between
Gravitational and Special Relativity').
In outlook, a visible mass is any mass of radius R.
The visible mass has to be capable of radiating light to be
seen in the universe. Its black hole M+ and R- equivalent at
the relativistic limiting barrier does not radiate light, and
so no longer physically exists in terms of basic electromagnetic
radiation.
Generally, a visible mass accelerated to relativistic
velocities cannot achieve a theoretical infinite visible mass,
and the velocity of the visible mass can never theoretically
equal the speed of light.
The interpreted statements in special relativity which say a
mass (obviously visible) continues to expand toward infinity,
and the velocity continues to the speed of light, are wrong, when
they do not take into consideration the black hole barrier effect.
The maximum velocity attainable by a visible moving mass, is
the speed of light reduced by the proportionate ratio of the
gravitational relativistic effect of the mass being accelerated.
The velocity barrier limit (maximum velocity) possible, is
restricted by the bounds achieved in special relativistic
effect when the mass has increased, and its radius has
contracted, to a point where the moving entity forms a
black hole and effectively disappears from view.
As already said, this point is easily calculated, as
being the velocity resulting when the speed of light
is divided by the proportionate effect of the mass's
gravitational relativistic effect.
This point will vary from mass to mass, and from radius to
radius per given mass, but will inevitably appear somewhere
before the speed of light is reached, when the visible mass
is being accelerated to relativistic velocities.
A further limiting factor is reached, when the original
mass factors and augmented mass factors are summed, to
reach an absolute prior limit at which the total mass
transforms into a black hole equivalent in single bumps,
which are proportionate factors of the Golden Harmonic
Ratio 1.618034.
?????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????????????????
? ????????????????? GENERAL CONCLUSIONS ????????????????? ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
The fundamental point of view adapted for much of the
preceding, is to consider that gravitational relativistic
effects are steady state. Ie., the gravitational source is
simply sitting there doing its relativistic thing.
And so there are no gravitational accelerations of a kind
which involve motions of points of center, when understanding
certain of the effect's basic properties, such as the effect
on the original mass of the gravity causing the effect.
Throughout the gravitational relativity explorations of Part 1,
the perspective was entirely from the perception of different
mass aggregates being squeezed within the same unchanged radius.
In practice, the only radius used was the radius of the
Sun, as it is presently measured empirically in this solar
system. That the Sun's radius can be presumed to be reduced
slightly by the relativistic effect of gravity has been taken
into consideration, but has not been explored through any of
the possible permutating effects that changes to the radius
might have. In short, the studies involved variable densities.
The very nature of gravitational relativity implies permuting
effects due to gravity on all of the parameters involved, for
instance on all of the terms in EQ W. The sheer magnitude of the
job of trying to explore all possible combinations of permutations
involving just R vrs M for this solar system, for instance, has
not been explored here.
Which leaves wide open a very important question. In the
circumstances so far described, there is no proof that the radius
of a mass aggregate is the bottom line through which important
gravitational relativistic manifestations are to be observed.
This in no way suggests that a proof should not be forthcoming.
It so happens that a constant radius (in this case the radius
of the Sun) is very convenient for displaying many important
manifestations of gravitational relativity and black hole
correspondences. It appears to hold together a thread of logic
though many physically dissimilar events, including standing stark
still (gravity relativity) and in motion (special relativity).
Such stark realism between the relativities would be a hard
(if not impossible) task to monitor if the confinement radius
was allowed to be mutable.
So, the Sun radius is freely used as a constant
for exploring different stark manifestations.
???????????????????????????????????????????????
??? MASS DENSITIES IN A CONSTANT RADIUS ?
???????????????????????????????????????????????
It is clear (as shown in many of the preceding demonstrations)
that the existing Sun radius might in some way be of fundamental
importance. Not necessarily in core physics of the universe as
a whole, but at least in core physics of the solar system.
This is seen in the interphased mass congress states involving
? units of Jupiter's mass, as discussed in Part 1.
In the various relativistic explorations, the Sun's radius has
been willfully maintained as a constant value through different
discrete changes in mass aggregates studied. (This applies to the
corresponding planet masses explored, and is not meant to apply
to any special relativistic effects explored).
Dynamically, a change in mass within the same radius usually
translates into a change in density of the aggregate.
In other words, density pressure may be a part of the cause
and effect, or at least may have originally been a part of
the cause and effect, prevailing at the time of this solar
system's formation.
This may be a clue regarding the unusual solar characteristics
observed; where different discrete units of mass (including
mass particles said to be a part of total mass aggregates)
are seen externalized as planets orbiting far from the major
field of the Sun.
The mystery is that the particles are orbiting well
beyond the significant radius of the inducing effect.
The external factors include planet masses which are a
part of the mass aggregate inducing significant effects.
One particular planet is Jupiter. Other planets are
clearly related to the induced effects, but their masses
do not seem to be included in the mass aggregates. These
planets are Venus and Mars.
It may be that concomitant to gravity relativistic
effects gained with the Sun's mass, special relativistic
effects are also gained. But rather than being produced
in the form of increased mass per se, the special effects
become produced in the form of velocity which can translate
directly into angular momentum, resulting in at least some
of the induced influences being flung into orbit thus carrying
away discrete units of relativistic effect in the form of
discrete quantities of angular momentum. This is only a
thought, probably ridiculous.
(In a casual thought, if a gravitational body also
induces a synonymous relativistic effect (motion) the
motion has no real way to go forth in itself, since
ideally all of the effect of motion is equidistantly
applied to a sphere (the gravitational body). In this
scenario, the motion portion is thrown off (externalized)
in order to be expressed).
??????????????????????????????????????????????
? A QUESTION REGARDING RELATIVISTIC ?
? MASS EFFECT AND QUASARS ?
??????????????????????????????????????????????
These following remark are purely conjectural.
Let's suppose that certain relativistic effects induced by
gravity seem to be incompatible with the basic gravity itself.
In other words there are two aspects to gravity: the original
(naked) gravity for any material, and the relativistic effects
caused by that gravity. In this supposition, some relativistic
nature cannot exist within the naked nature, and so is
externalized at long distance.
The externalizing is guessed as either by a throwing off
(forcibly casting forth) or by a remake (as if in leaping
from here to there, where 'there' is a predetermined position
in some kind of latent underscore pattern involving the gravity
field). (In high energy physics, many sub atomic particle
interactions are depictable as occurring simultaneously in two
places at once, where an event at one place directly effects
the event in another place even though nothing but thought
can transfer between the two places). A third form of ejection
might be by the simple virtue of an outthrow of discrete bits
by angular momentum.
In the workings of gravitational relativity, several things are
at issue. There is an original mass, plus the original mass's
augmentation due to the relativity of the mass's gravity. There
can also be more mass added into the conglomerate at any time.
Which results in a hike in the augmentation effect due to
strengthened relativity.
It can be supposed that if an increase in mass takes place within
a given radius, resulting in a hiked relativistic mass augmentation
due to the added mass, which in turn causes jitters so that
something of the hike has to be expunged or externalized from the
gravity field which is generating the effect in order to satisfy
an esoteric yearn to solve the jitters, then where added mass is
accreting into a large black hole some of the relativistic gain
is transferred to an external position outside the black hole.
Since very high energy effects are involved with the black
hole anyway, it is not difficult to picture that the expunging
can appear highly energetic. What the mechanism is that could
transfer the effect to an external place is not here conjectured
but can be supposed. For instance:
A long arm recurrence (here and also there) is one mode.
An intense radiating away (or bleeding away) of some of
the change upon the event horizon boundary, in alternative
to allowing a change to go ahead in the relativistic regions
of the boundary size itself, is another mode. This is made more
viable if it is suggested that the black hole yearns to maintain
some form of internal density which has no further relativistic
influence inside the black hole.
And finally, a conversion of units of intrinsic spin
as energy, (conversion from spin to propagational energies),
is another, if possible.
??????????????????????????????????????????????
? A QUESTION REGARDING RELATIVISTIC ?
? EFFECT ON THE GRAVITATIONAL CONSTANT ?
??????????????????????????????????????????????
There is also the prospect that the gravitational constant itself
is modified by the relativistic effect of gravity. In retrospect,
it is not readily apparent as to whether the gravitational constant
would weaken, or strengthen, relativistically, given larger and
larger masses. The present day mode of thought is to consider that
the gravitational constant might grow relativistically stronger.
On the other hand, Equations Y to Y-2 above suggests that
the gravitational constant relativistically weakens through
increasing mass aggregates.
On yet another hand, it has not been proven that a mass
relativistically increases (as opposed to decreases) by
gravitational relativity. A stable picture should ensue,
albeit not exactly the same as the picture described in
Equations T through Z-11-4, if a mass decreases by its
gravitational effect, such that the mass's confining
radius might increase, or decrease, and the gravitational
constant also might increase, or decrease, etc.
Such possibilities are not considered in the above shown mass
congresses involving the Sun and certain planet masses. If the
gravitational constant is in fact modified by relativity, then
the apparent mass of the Sun is still valid, but the original
mass should not be precisely that as determined by the apparent
mass MM, minus the apparent mass times the effect; as shown in
EQ W-1.
In fact all of the parameters of Equation 1 below in APPENDIX B
(except for the speed of light) might be in states of modification.
These parameters include G and M, where a mutable value of G therefore
is internally influencing the value of M.
In any case, the resulting gravitational relativistic mass
congresses between the Sun and planets as viewed herein are
in their resultant apparent states (involving the masses as
seen in the domain of the solar system and empirically measured).
And finally, the direct tie-ins between gravitational and
special relativity are balanced correctly anyhow, according
to the parameter choices selected for the preceding, to
infer then portray their handshake nature.
In a casual thought, if a gravitational body also induces
a synonymous relativistic effect (motion) the motion has no
real way to go forth in itself, since ideally all of the
effect of motion is equidistantly applied to a sphere (the
gravitational body). In this scenario, the motion portion
is thrown off (externalized) in order to be expressed.
It is not hard to speculate that the special relativistic
mass gain for the stationary object (gravity source) can be
(at least in part) thrown off in the form of energy, since
e=mC?. In which case a lot of energy will be visible per
small quantities of involved gain in mass.
In this speculation, there is a pure (rather than nuclear)
conversion of mass to energy.
In unstated allusions are hints that gravity and special relativistic
effects work hand in hand, with perhaps the special relativity effects
being more and more suppressed the higher the gravity. But as already
said, any special relativity associated seems to be incompatible within
the naked gravity itself and so ends up externalized (for instance) as
certain planets, as if a velocity is induced in a gravity mass at rest
which can leave its source, via angular momentum in the velocity.
??????????????????????????????????????????????
? A QUESTION REGARDS THE GRAVITATIONAL ?
? CONSTANT AND THE GOLDEN HARMONIC RATIO ?
??????????????????????????????????????????????
Whereas in another conjectural possibility, going in the other direction,
it may be possible that the apparent quantum jump in relativistic effects
seemingly embodied in operators involving the golden section ratio (the
golden harmonic), do not actually occur in the physical universe.
For instance if the universal gravitational constant did change in
value under increasing relativistic influence, it may result in a
situation where such things as mass and space increase smoothly toward
infinity after all, with the quantum leap from a plateau straight to black
hole parameters smoothed out or voided by relativistic changes in the power
of the universal gravitational constant.
Ho hum, speculations can be rather boring.
?????????????????????????????????????????????????????????????
????????????????????????????? APPENDIX A ?????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
? ELEMENTARY PARTICLE MASSES ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
In high energy physics experiments, particles such as the
electron or Proton are being accelerated to velocities said
to be virtually at the speed of light.
How is this possible?
This is possible because the Mass/Radius ratio of the proton
(as an example) is extremely small, compared to the Mass/Radius
ratio of the Sun for instance. The Mass/Radius ratio of the Sun is:
(Mass 1.991 x 10 to 33 grms) / (Radius 6.963 x 10 to 10 cms)
= (2.859 x 10 to 22 grms/cms)
which itself is very small compared to the ratio of a black hole
having the Sun's radius, in which the Mass/Radius ratio is then:
Mass = (C? x R) / 2G = (4.689 x 10 to 38 cms)
And:
(Mass 4.689 x 10 to 38 grms) / (Radius 6.963 x 10 to 10 cms)
= (6.735 x 10 to 27 grms/cms) = CR
Note that value (6.735 x 10 to 27 grms/cms) = CR is actually
a physical constant for every black hole, and is equal to the
ratio of the speed of light divided by twice the universal
gravitational constant, as in: (C?/2G) = CR = (Mbh/Rbh)
when Mbh and Rbh are the Mass and Radius (event horizon) of
a black hole, C is the speed of light, and G is the universal
gravitational constant.
When, otherwise, a normal M and R are transfigured by special
relativity into a new black hole having mass M+ and radius R-,
then: CR = (M+/R-), where, CR still has the constant value:
(6.735 x 10 to 27 grms/cms).
In the large scale world of normal events the magnitude of
the Sun's mass at (10 to +33 grms) is well above the magnitude
of the Sun's radius at (10 to +10 cms).
In the world of the very small, the situation is
quite reversed. For example the mass of the proton is:
1.672 x 10 to -24 grms
whereas its radius is reverse in magnitude,
in the much larger range said to be about:
1.32 x 10 to -13 cms.
This produces a Mass/Radius ratio (proton Mass/proton Radius) of:
= 1.239 x 10 to -11 grms/cm.
Clearly, a proton will have to accelerate to an extremely
high velocity, virtually to the speed of light, in order
for special relativistic effects to transfigure the proton's
effected mass M and radius R into the (M+/R-) = CR parameters
of a new black hole.
The Mass/Radius ratio of the proton will have to grow by a
magnitude of (5.435 x 10 to the 38), in order for the accelerated
proton to take on the look of a black hole having mass M+, and
radius R-, and a (M+/R-) ratio equal to CR.
A calculation to determine what velocity the proton needs to
move in order for the transfiguration, is impossible to complete
with devices having mediocre accuracies good to only (say) 13
significant figures.
The calculation to determine the proton's velocity first requires
knowing what the gravitational relativistic effect Eg is for the
proton's mass and radius. Effect Eg is too small by many magnitudes
to be mechanically calculated by a device of 13 significant figures.
Given a device with greater accuracy, the resulting Eg effect for
the proton is divided into the speed of light, to give the velocity
at which the proton must travel to relativistically transform into
a black hole. The velocity will be the same as the speed of light
to many significant figures, before the digits begin to deviate.
(Unless there is (previously unsuspected) a gate in the velocity
of light, at which a particle (for instance a proton) might in fact
make a quantum leap to black hole magnetudes at a point that is at
some measurable factor less than a total 100 percent of the speed
of light).
???????????????????????????????????????????
? Proton Comparative Mass Density ?
???????????????????????????????????????????
To give a comparison on just how nebulous is the mass
density of the Proton (how little in the way of gravity
that Proton matter presents), the mass density of a Proton
is on par with about 1 gram of matter wisping in a shell
whose width is equivalent to 10 times the full diameter
of the orbit of the Moon around Earth.
If the on par Proton mass were gathered together for the protion
which occupied the actual orbit of the Moon, it would be a moon
weighing about .48 grams circling the Earth.
?????????????????????????????????????????????????????????????
????????????????????????????? APPENDIX B ?????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
? BASIC EQUATIONS ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
Advanced details of a black hole, such as a paradigm model
of a charge membrane for instance, are not considered.
?????????????????????????????????????????????????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? RELATIVISTIC MECHANICS ?
???????????????????????????
EQUATION 1
??????????????????????
? 2G M Finding gravitational relativistic
Eg = ? 1 ? ????? effect Eg, for a given mass M and
\? C? R a given radius R
EQUATION 2
(1 ? (Eg)?) x C? R Finding mass M for a given
M = ?????????????????? radius R and a given
2G relativistic effect Eg
EQUATION 3
2G M Finding radius R for a given
R = ?????????????????? mass M and a given gravitational
C? (1 ? (Eg)?) relativistic effect Eg
EQUATION 4
2G M Finding the Schwarzschild
R' = ??????????????? radius R' of a black hole's
C? event horizon. When effect
E = 1, then factor (1 ? (E)?)
is 0, which drops from EQ 3
leaving EQ 4
EQUATION 5
C? R' Finding mass M' needed for a
M' = ??????????????? black hole whose Schwarzschild
2G radius is given as R'
?????????????????????????????????????????????????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? GRAVITATIONAL MECHANICS ?
????????????????????????????
EQUATION 6
V? R Finding the mass M for
M = ??????????????? sustaining a body orbiting the
G mass at a given velocity V at
a given orbiting distance R
EQUATION 7
G M Finding the orbit R of a
R = ??????????????? body around a given mass M
V? at a given orbital velocity V
?????????????????????????????????????????????????????????????
????????????????????????????? APPENDIX C ?????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
? PURE MASS CONGRESS ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
This information is presented as a separate tableau and
has no self evident bearing on any of the explorations
and conclusions of the above statements. The following
shows that generally:
(? THE SUM OF THE MASSES OF MERCURY, VENUS, EARTH, MARS),
PLUS THE MASS OF THE MOON, EQUALS THE MASS OF THE EARTH.
(? the sum of masses N1 to N4) + N5 = N3
TABLE 10
Masses + N1 Mercury = .33020 x 10 to 27 grms
+ N2 Venus = 4.8683 x 10 to 27 grms
+ N3 Earth = 5.9760 x 10 to 27 grms
+ N4 Mars = .64181 x 10 to 27 grms
??????????????????????????????????????????????????
= 11.81631 x 10 to 27 grms
??????????????????????????????????????????????????
? = 5.908155 x 10 to 27 grms
??????????????????????????????????????????????????
+ N5 Moon = .07350 x 10 to 27 grms
??????????????????????????????????????????????????
Equals N3x Earth = 5.981655 x 10 to 27 grms
????????????????????? ?????????????? ???????????? ???????? ????
Inequality N3x - N3 = .005655 x 10 to 27 grms
There is an extra (+ .005655 x 10 to 27 grms) in the N3x
result, which is unexplained. There is no other Moon in
the inner region of the solar system for instance.
The aggregate mass of the asteroids seems to be too
small by a factor of 10 to be this inequality. So the
extra (.005655 x 10 to 27) does not meaningfully represent
the mass of the asteroids. What the mass inequality may
represent is not clear at all.
?????????????????????????????????????????????????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
? GENERAL MASS CONGRESS (summary)
??????????????????????????????
The Sun's mass plus ? the mass of Jupiter added, can be shown
to induce a gravitational relativity mass increase effect which
is exactly equal to the mass difference between the planets Venus
and Mars.
??????????????????????????????????????????????????
? 2G x (Sun mass + 1/2 Jupiter mass)
(Sun effect ratio) = ? 1 ? ??????????????????????????????????
\? C? x R
C = Speed of light
G = Gravitational constant
R = Radius of the Sun
K (Mass augmentation) = Sun mass - [Sun mass x (Sun effect ratio)]
K (also equals) = Venus mass - Mars mass
The same result is handled (in a slightly different way)
in the section beginning with TABLE 1 of file RELATIVE.1 .
See TABLE 11 next below.
TABLE 11
????????????????????????????????????????????????????????????
? K = 4.226490 x 10 to 27 grms ?
? = (Venus mass - Mars mass) ?
????????????????????????????????????????????????????????????
? C = 2.99792458 x 10 to 10 cms/sec ?
? G = 6.6720 x 10 to -8 cms3/grms sec? ?
? R = 6.96265 x 10 to 10 cms ?
????????????????????????????????????????????????????????????
? ?
? Planetary masses Data is from Table 1 in ?
? the file RELATIVE.1 ?
? ?
? Moon = .0735 x 10 to 27 grms ?
? ?
? Venus = 4.8683 x 10 to 27 grms ?
? Earth = 5.976 x 10 to 27 grms ?
? Mars = 6.4181 x 10 to 26 grms ?
? Jupiter = 1.901 x 10 to 30 grms ?
? ?
? Sun = 1.9888 x 10 to 33 grms ?
? ?
????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
????????????????????????????? APPENDIX D ?????????????????????????????
? ????????????????????????????????????????????????????????????????????? ?
? FOOTNOTES ?
? ????????????????????????????????????????????????????????????????????? ?
?????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????????
??????????????????????????????????????????????
????????????????????????????? Footnote 1 ?????????????????????????????
??????????????????????????????????????????????
????????????????????????????????????????????
??? RELATIVITY EQUIVALENCE PRINCIPLE ?
????????????????????????????????????????????
EQUATION Z-21
1 - Eg? = 1 - Es?
One minus the square of gravity's relativity effect,
equals one minus the square of special relativity's effect.
?????????????????????????????????????????????????????????????????
EQUATION Z-22
1 1
?????????? = ??????? = Nx
1 - (Eg)? (Es)?
The reciprocal of one minus the square of gravity's relativity
effect, equals the reciprocal of the square of special relativity's
effect.
This equality is equal to the ratio of a gravitational mass divided
into the mass equivalent of a silent black hole partner for the
gravitational mass.
??????????????????????????????????????????????
????????????????????????????? Footnote 2 ?????????????????????????????
??????????????????????????????????????????????
There is recent speculation that events in electroweak theory and
gravitational theory may converge to similar kind at very small
distances of the order of (10 to -28 cms) to (10 to -33 cms), said
to be possible at the time of a so called big bang. Whether or not
the unified field behaviors as disclosed in the above equations are
favorable or distasteful to such a big bang outlook is not in any
way considered to be of our concern, here.
??????????????????????????????????????????????
????????????????????????????? Footnote 3 ?????????????????????????????
??????????????????????????????????????????????
In use of the Sun's radius as a constant confinement delineator for
various mass aggregates and equivalent black hole masses, it is
acknowledged that the amount of extra mass poured into the existing
size of the Sun has to be very large to make a black hole.
For example the amount of mass is about 235,000 times the mass of
the Sun, poured into the space occupied by the Sun, to make a black
hole. This is of course physically unrealistic, (that that mass can
pour into the Sun and the Sun stay the same size). But having a
constant radius makes it far easier to keep track of various effects.
The physical universe is actually quite different. For instance the
radius of the Sun will dramatically expand with any appreciable amount
of mass poured into it.
But this is iffy. For example if the extra mass is iron, the Sun's area
will expand according to high material density. If the matter is helium
or hydrogen, the enlargement of the Sun's radius will be substantially
more.
In either case, since the radius is expanding (with more matter
poured in), a black hole mass plateau will be eventually reached
at a much different enlargement in mass than the factor of 235,000
times mentioned above. As you can see, pinning down parameters into
'look and see' constants, with this sort of thing going on, is like
trying to pin down the behavior of silly putty.
And so events herein have been scrutinized in detail from the point of
view of a single unchanged basic radius (the Sun radius), used as a
convenient point of reference to compare significant related events
that involve that single radius.
??????????????????????????????????????????????
????????????????????????????? Footnote 4 ?????????????????????????????
??????????????????????????????????????????????
The Golden Harmonic Ratio 1.61803398875, cited in this disclosure, is
an absolute number value gained as (? of ?5) plus .5. This number is
also known as the Golden Section. The number can functionally permutate
through a bewildering array of directions on its own, with many
particular permutations appearing in the construction of 5 sided
geometrical figures. A particularly well known physical manifestation
of the Golden Section is the proportion of a Golden Rectangle. Other
well known manifestations include spirals and progressions occurring
in nature, some based on the Fibonnaci number series. These are said
to include galaxy spirals and Bode's Law for the solar system, however
some researchers think the astronomy occurrences appear to be as much
a case of co-incidence as anything.
??????????????????????????????????????????????
????????????????????????????? Footnote 5 ?????????????????????????????
??????????????????????????????????????????????
The Constant Ratio CR cited above as being M+/R- = C?/2G
also gives instant readout on such curiosity questions as:
1. How much mass is contained in a black hole whose radius
is 1 cm? The answer is:
6.735275620 x 10 to 27 grms In that:
C? R Finding mass M needed for a
M = ??????????? black hole whose Schwarzschild
2G radius is given as R = 1 cm
Note that the mass has the same
digital value as ratio CR
2. What confinement radius is needed for a black hole whose
mass is 1 grm? The answer is:
1.484720234 x 10 to -28 cms Note that this is the digital
reciprocal of the value of the
mass M of question 1, in that:
2G M Finding the Schwarzschild radius
R = ?????????? R event horizon of a black hole
C? whose mass is 1 grm
??????????????????????????????????????????????
????????????????????????????? Footnote 6 ?????????????????????????????
??????????????????????????????????????????????
In the most unusual circumstance of a velocity ratio V/C being
equal to a mass proportional ratio M1/M2, then gravitational
relativistic effect Egs is equal to ratio M2/M1.
For instance, let the ratio of one mass M1 divided
by a smaller mass M2 be called Rn.
????????????????? ???????????????
? (C/Rn)? ? V?
Then: Ess = ? 1 - ??????? = ? 1 - ????
\? C? \? C?
And: Egs = 1/Rn
??????????????????????????????????????????????
????????????????????????????? Footnote 7 ?????????????????????????????
??????????????????????????????????????????????
In case there is a concern over what has been done above, (in the
conjecturing of major effects as seen wrapping around changes in
the rest state of masses through two different synonymous modes of
relativity), there are no rules that exclude a direct synonymous
tie-in between both gravitational and special relativistic effects.
For example, it has been experimentally confirmed that time slows
in the proximity of a gravitational field. A main question which
can be asked is:
At what velocity does a mass have to be moving, to induce a
slowing of time (time dilation), that is equivalent to the
field effect from the gravity generating a relativistic
effect of equal magnetude on the flow of time?
The time dilation effect of a velocity in special relativity is
straight forward. That is, at a given velocity, events in time
for the moving object will seem slowed by a specific amount as
seen by a stationary observer.
In the case of gravity effect, the situation is more ambiguous.
The effect of time dilation depends on where the object is in the
vacinity of the field generating the effect. Closer to the field
means a greater time dilation. But in large scale objects such as
the Earth or more so the Sun, closeness empirically means close
to the surface, for example, rather than close to a mathematical
data point or to a fixed velocity.
In our explorations above, real time positions moving here or there
in the embraces of a varying gravity field are not at all in the
picture. The basic 'need to know' speaks through simple statements
consisting of 'how much mass' in 'how much radius' to result in 'how
much effect' in the gravity will effect time.
The main point of view has been in terms of gravity as a mass source
extending in a boundry termed the gravity body's radius. In this view,
events can be measured from the radius and extending outward from the
radius, according to a mass total located at the radius, where the
radius itself is measured from a single point of center.
In questioning a mass augmentation effect in the gravity, the issue
can be more clear cut. Specifically, given a finite mass and a finite
radius, what gravity relativity effect is generated, and how much
does the effect increase the original mass generating the effect?.
From this steady stateness, it is easy to ask across to special
relativity wishing to know what velocity is required to generate
an identical effect.
However, in closer introspect, a greater question has also been asked.
And that is, given a mass enhancement and space contraction in special
relativity, at what velocity does a mass have to be moving in order
for it to transfigure into a black hole? Looking at things from another
point of view the question can be put in yet another way; to wit:
At what velocity does the mass have to be moving in order
for special relativistic effect (increasing the mass's mass
and collapsing its radius) to cause the mass's flow of time
to come to a standstill? The answer is found in an M+/R- ratio,
which is calculated through special relativity using the mass's
gravitational effect to state the equivalent relative velocity.
This type of thinking is out in the open in the material of Part 4.
It is summarized in the relationships enclosed in TABLE 8 under
'Pure Math Connectors' above.
??????????????????????????????????????????????
?????????????????????????????? FINISHED ??????????????????????????????
??????????????????????????????????????????????
??????????????????????????????????????????????????????????????????
Planetary Data is from the following reference source:
UNIVERSE by Don Dixon, Houghton Mifflin Co.,
Boston, 1981 (References found at
the back of the book)
??????????????????????????????????????????????????????????????????
Signed: Rhae. S. Livingstone
Address: 78072, Cityview, Nepean, Ont, Canada K2G 3J0
Phone number: Area code: 613 820-9450
(C) 1990 Introduction to Mass Increases By Gravitational Relativity.
Rhae S. Livingstone. Canada.
Copyright March 16, 1990
All rights reserved.
Peace Power and Plenty everyone.
ALL DONE