Preface:
In the zero origin universe, an anisotropy in the gravity force is generated by motion to and from a gravity source because dimension is moving inward into the gravity well at a rate determined by the mass within, and the process is updated at the speed of light from the gravity source. As a consequence, the force applied by the shifting dimension reduces to zero for light speed motion toward the source, and doubles for light speed motion in the up direction.
The original equation representing the effect of the anisotropy on an
upward moving mass relative to a gravity source was given as
((c+v)^2/c^2)^.5*G*M/r^2-(G*M/r^2), while
((c-v)^2/c^2)^.5*G*M/r^2-(G*M/r^2) represented its effect on a downward
moving mass. I include them in this format to demonstrate the basis of the
simplified equation, v/c(GM/r^2). Physical sign manipulation for the up
and the down motion directions is unnecessary using signed radial velocity
relative a gravity source (- in and + out).
As a natural consequence of the above, any motion at all relative to the matter of the universe will also generate a gravity anisotropy.
I had previously based my calculations for the universe generated anisotropy on v/c(G*Mu), where Mu is the mass equivalent of the universe at a 1 meter radius in the plane of relative motion. The value 300000 kg at a 1 meter radius along the line of motion was chosen because it's compatible with the Pioneer Anomaly, which has yet to be explained. But that system was obviously going to cause confusion.
This program is designed to generate mass per radius combinations that align with the 8.3e-10m/sec^2 anisotropy generated by Pioneer's motion relative to the mass of the zero origin universe. M/r^2 replaces Mu. Copy-Paste it directly off this screen.
'-----Program start--------
DEFDBL A-Z
CLS
c = 300000000#
G = .00000000006673#
pi = 3.1416#
v = 12500# ' Pioneer's speed along it's trajectory.
aa: LOCATE 8, 1
PRINT " Radius at which the mass of the universe is to be stored"
INPUT " (distance to the big bang = 1.23e26 meters)"; r
IF r = 0 THEN END
M = 300000# * r ^ 2
u = v / c * (G * M / r ^ 2)
LOCATE 12, 1
PRINT M; "kg. Mass equivalent of the universe. "
PRINT r; "meters. Radius at which the mass is stored. "
PRINT v; "m/sec. Pioneer's relative velocity. "
PRINT u; "m/sec^2. Generated anisotropy. "
LOCATE 9, 47: PRINT " "
GOTO aa
'----Program end------------
These results were generated by the program.
300000 kg. Mass equivalent of the universe.
1 meters. Radius at which the mass is stored.
12500 m/sec. Pioneer's relative velocity.
.000000000834125 m/sec^2. Generated anisotropy.
3D+17 kg. Mass equivalent of the universe.
1000000 meters. Radius at which the mass is stored.
12500 m/sec. Pioneer's relative velocity.
.000000000834125 m/sec^2. Generated anisotropy.
3D+37 kg. Mass equivalent of the universe.
1D+16 meters. Radius at which the mass is stored.
12500 m/sec. Pioneer's relative velocity.
.000000000834125 m/sec^2. Generated anisotropy.
3D+57 kg. Mass equivalent of the universe.
1D+26 meters. Radius at which the mass is stored.
12500 m/sec. Pioneer's relative velocity.
.000000000834125 m/sec^2. Generated anisotropy.
The final result has the entire mass of the universe stored at almost the radius to the big bang, where, in that universe, the expansion rate has reached the speed of light. No anisotropy could be generated beyond that point. To achieve a satisfactory result the matter content of the universe would rise to infinity at that radius.
But that has nothing to do with the point I'm trying to make, that there is one radius that could correctly represent the mass of the universe, and at that radius, Pioneer's motion will still generate exactly the same anisotropy as it does for the above examples and all other possible examples.
v/c(G*Mu) is obviously the most convenient formula for calculating the universe generated anisotropy, so I'll continue using it.
The designated 300000 kg mass along the line of relative motion is representing the effect from the entire hemispheres of matter in each direction along that line. i.e. For an orbiting body, the anisotropy is constant while tangential speed remains constant.
____________________________________________
The anisotropy generated by the Sun's 220000 m/sec orbital speed around the galaxy center is v/c(G*Mu) = 1.467e-8 m/sec^2. If the process is entirely elastic, the Sun must be traveling fast enough to build the required centrifugal force to counteract that added force.
The next graph was generated by an extension of the following Qbasic program. The lower dark blue line intersects with the Sun's true orbital speed of 220000 m/sec. But the orbital speed there is found to be around 278 times less than is required to counteract the anisotropy, as it is everywhere else.
The original graph was based on false logic, hence the update.
The galaxy mass was presumed to be uniformly distributed throughout the disc, forcing the Newtonian gravity rate for each radii to be constant because the mass contained within each radius reduces at a squaring rate per radius decrease. Since the base line on the graph represents the calculated speeds, while the graph plots depict only the variation from that line, wherever the plot calculated according to the mass distribution in the real galaxy goes, the graph plot will follow.
The results is in fact almost identical if the program is set up so that the galaxy mass diminishes with increasing radius.
'----Program start---------
' Gathered info:
'Sun's velocity = 220km/sec. It's supposed to be 160km/sec.
'Sun radius is 8.7 kpc or 27000 ly from the galactic center.
'The mass, including the dark matter, must be about 1e+12 times
'the mass of the Sun, with considerable uncertainty.
'With no DM the galaxy mass is equal to 1e+11 Suns.
'---------
'So, within the Sun's radius of 27000 light years, in the 72000
'light year radius galaxy, there are 1e+11 / (72000^2 / 27000^2)
'= 1.4e+10 Sun masses, in a galaxy of uniform mass distribution
'of course.
DEFDBL A-Z
CLS
pi = 3.1416#
G = .0000000000667#
PRINT " These are the parameters within which the Sun's orbit"
PRINT " around the galaxy must accommodate the gravity anisotropy"
PRINT " generated by motion relative to the mass of universe."
M = 1.99D+30 * 324100000000# 'Sets the galaxy mass to align with
'the Sun's expected orbital speed of 160 km/sec.
PRINT M; "total galaxy mass. "; M * 10; "if DM is included."
sa = 70000 'light year galaxy radius.
sb = 27000 'light year Sun orbit radius.
ml = 1 'Multiplier initially set for the Sun's radius.
aa:
LOCATE 6, 1
Mx = (M / (sa ^ 2 / sb ^ 2)) * ml ^ 2: r = 2.5D+20 * ml: f1 = 0
' Mx = 1.99D+30: r = 150000000000# * ml: GOSUB ad: f1 = 1
'Swap the ' switch on the above two lines for the solar system.
PRINT Mx; "kg mass inside the"; r; "meter orbit radius."
Mu = 300000#
c = 300000000#
v = (G * Mx / r) ^ .5#
w = v
'w can be any number at this point. It's later corrected, and defined.
vx = v
'vx is later updated to the actual orbital speed.
newton = G * Mx / r ^ 2
PRINT newton; "Newtonian gravity rate." ' is always the same
'in a galaxy of uniform mass distribution throughout the disc.
ab:
'This routine is cycled through until centripetal and centrifugal forces
'are near enough to being equal. Each updated orbital speed affects the
'anisotropy, until the current update is almost the same as the last.
vx = w
anisotropy = vx / c * (G * Mu)
cpetal = newton + anisotropy
cfugal = vx ^ 2 / v ^ 2 * newton 'total centrifugal force.
w = SQR(cpetal * v ^ 2 * r ^ 2 / (G * Mx))
'w holds the current orbital speed, which is progressively updated
'until the correct speed is found. The anisotropy is affected by every
'speed update.
IF w = wf THEN GOTO ac
wf = w
va = v + ((w - v) * .0036) 'actual speed.
'The .0036 multiplier was chosen to suit the Sun's true orbital speed.
'The assumption is that the same ratio between actual and calculated
'speeds will remain constant for all scenarios.
LOCATE 8, 1: PRINT anisotropy; "anisotropy per"; vx; "m/sec speed."
PRINT va / c * (G * Mu); "anisotropy for the actual orbital speed. "
PRINT
PRINT " These two results should end up being almost equal."
PRINT cpetal; "total centripetal force."
PRINT cfugal; "m/sec^2 total centrifugal force. "
PRINT
PRINT w; "orbital speed required for a sustainable orbit "
PRINT " (including anisotropy)."
PRINT v; "calculated orbital speed with no anisotropy (normal). "
PRINT va; "actual orbital speed. "
PRINT
PRINT w - v; "m/sec. Stable orbit speed - normal speed. "
PRINT va - v; "m/sec. Actual speed - normal speed. "
'PRINT (va - v) / (w - v) * 100; "%"
' DO: LOOP UNTIL INKEY$ <> ""
'Remove the ' switch on the DO statement, then with
'key pushes, step through this routine.
GOTO ab
ac:
PRINT
IF f1 = 0 THEN INPUT " Radius multiplier (Sun orbit radius = 1)"; ml
IF f1 = 1 THEN INPUT " Radius multiplier in AU (Earth=1)"; ml
IF ml = 0 THEN END
CLS
GOTO aa
ad:
LOCATE 1, 1
PRINT " These are the parameters within which the Earth's orbit "
PRINT " around the Sun must accommodate the gravity anisotropy "
PRINT " generated by motion relative to the mass of universe. "
PRINT " "
M = 1.99D+30
PRINT M; "Sun's mass. "
RETURN
'-----Program end------
The Sun and every individual clump of matter in the universe forms a closed gravitating system which has been established over perhaps billions of years. Regardless of how distant the components may be, their past presence is right here, now, and vice versa. So the anisotropy is immediately generated and its consequences are immediate, even though the reaction to those consequences can take billions of years. If the anisotropy is inelastic, energy must be carried away by something and the only available something is the gravity link from everywhere to the Sun.
In the animation, the orbiting Sun forms an individual closed gravitating system with every piece of matter in the two hemispheres of the universe in the plane shown. Consider only the plane between the two masses which is through the galaxy center and perpendicular to the orbit path. Clearly, in that relationship with the Sun, the anisotropy generated varies between zero and the maximum for the orbit velocity. The action of gravity in that system can only affect the Sun in a very precise direction. The Sun is slowed by its motion away from matter on one side and slowed by its motion toward matter on the other. And that slowing is occurring exactly along the line across the orbit diameter.
The main purpose of the animation is to demonstrate that, in any specific plane, by the time the Sun has reached the far side of its orbit, the orbit radius will have shrunk by exactly the slowing applied by the anisotropy, in that plane, over the time of the journey.
The anisotropy generated in any specific plane is .637 of the total, or anisotropy / (pi/2). I had previously made the mistake of applying that divisor to the total, which was wrong. And it altered the results significantly.
The anisotropy generated by the Sun's orbital speed of 220000 m/sec is v/c(G*Mu) = 1.467e-8 m/sec^2. The anisotropy remains constant while the Sun's orbital speed, and the mass contained in the two relevant hemispheres as the plane of the Sun's trajectory indexes around, remain constant.
If the anisotropy is inelastic, in each half cycle (1.1e+8 years, 3.5e+15 seconds), the Sun has fallen to the galaxy center by 3.5e+15 * 1.467e-8 = 51345000 meters, or 51345 km in 1.1e+8 years. Which is 466773 km in a billion years. That's not really a problem is it.
Removing the switch ' preceding Mx = (etc), sets the above program up so that the same effect can be calculated for the solar system. The Sun replaces the galaxy, while the planets take the place of the stars.
These are the anomalous orbital speed increases for the planets, for 100% elastic, and .36% elastic anisotropies. .36% results from dividing (the actual orbital speed minus the calculated speed) by (the orbital speed required to counteract the anisotropy minus the calculated speed).
AU 100% elastic .36% elastic
Neptune 30.06 .15 m/sec 5.41e-4
Uranus 19.18 9.59e-2 3.45e-4 m/sec
Saturn 9.54 4.77e-2 1.72e-4 anomalous
Jupiter 5.20 2.60e-2 9.36e-5 orbital
Mars 1.52 7.60e-3 2.74e-5 speeds.
Earth 1.00 5.00e-3 1.80e-5
Venus 0.72 3.60e-3 1.30e-5
Mercury 0.39 1.95e-3 7.02e-6
The perihelion advance of Mercury is partially caused by the gravity anisotropy, so the link is an integral component of this page because it gives a reason for the very diminished elasticity in the average of all Sun-universe closed gravitating systems.