10 to the minus 36th the radius of the solar system.... General Relativity and Quantum Cosmology, abstract gr-qc/0104064
From: "Slava G. Turyshev"
Date (v1): Thu, 19 Apr 2001 22:42:49 GMT (834kb)
Date (revised v2): Tues, 15 May 2001 20:55:26 GMT (835kb)
Date (revised v3): Tues, 5 Feb 2002 21:05:21 GMT (851kb)
Study of the anomalous acceleration of Pioneer 10 and 11
Authors:
John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, Slava G. Turyshev
Comments:
RevTeX, 54 pages, 18 figures, and 3 tables. Additions and modifications for PRD publication
Report-no: LA-UR-00-5654
Sub-class:
General Relativity and Quantum Cosmology; Space Physics
Our previous analyses of radio Doppler and ranging data from distant spacecraft in the solar system indicated that an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a magnitude $a_P\sim 8\times 10^{-8}$ cm/s$^2$, directed towards the Sun (anderson,moriond).
Much effort has been expended looking for possible systematic origins of the residuals, but none has been found. A detailed investigation of effects both external to and internal to the spacecraft, as well as those due to modeling and computational techniques, is provided. We also discuss the methods, theoretical models, and experimental techniques used to detect and study small forces acting on interplanetary spacecraft. These include the methods of radio Doppler data collection, data editing, and data reduction.
There is now further data for the Pioneer 10 orbit determination. The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. [For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.]
With these data sets and more detailed studies of all the systematics, we now give a result, of $a_P = (8.74 \PM 1.33) \times 10^{-8} \{\rm cm/s}^2$. (Annual /diurnal variations on top of $a_P$, that leave $a_P$ unchanged, are also reported and discussed.)
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Hi David:
In the two/ sphere concept, gravity is a Planck Realm phenomenon caused by a micro singular matrix at the lowest levels of scale in the cosmos.The "CBR" is the 2.73 Degree K photonic "other side" of this phenomenon as observed from our frame.
I'm looking for a "gravitational" force equal to about 10 to the minus 8th of the gravitational attraction of the Sun at a distance of 10 billion kilometers.
Lets start with a sphere of space with a radius of 10 billion Km. Since the tide of singular gravitation rises close to massive bodies, lets assume we will need an average of say 10 to the minus 36th....closer to 10 to the minus 33rd near the sun and 10 to the minus 40th in intergalactic space....
OK, what is the gravitatational attraction of a black hole with an event horizon radius 10 to the minus 36th the volume of a sphere of "space" with a radius of 10 Billion Km?....at a distance of 10 Billion Km? Is it 10 to the minus 8th that of the parent body?..(the sun)
We are going to be off, for singularity in space pulls from every direction, and as a spacecraft departs the solar system, the influence of the suns "gathering effect" diminishes...however, even at 10 billion Km. The sun is still the dominant influence....
Thanks Again,
Sam Cox
Response from David, Monday, 2/18/02
"OK, what is the gravitational attraction of a black hole with an event horizon radius 10 to the minus 36th the volume of a sphere of "space" with a radius of 10 Billion Km?....at a distance of 10 Billion Km? Is it 10 to the minus 8th that of the parent body?.. (the sun)"
g ~ -GM/r2
GM = r0c2/2
Therefore:
g = -(1/2)(r0c2/r2)
V0/Vs = (r0/rs) 3 = 10-36
rs = 1013
r = 1013m
r0 = rs
so:
g = -(1/2)(V0/Vs)1/3 (c2/r)
g = -(1/2)(10-36)1/3 [(3x108)2/1013]m/s2
g = -4.5x10-10m/s2
AUTHORS COMMENTS
First note the difference in units used by Dr. Anderson (Centimeters) and David (Meters). Upon appropriate conversion, Davids work, based on the average figures I gave him, works out to -4.5x10-8Cm/sec2. The minus sign indicates a deceleration...a force acting toward the Sun.
This is astounding! Without complex computers, and working on a remote island with only averages, coming up with such a number is the equivalent of hitting the ball over the center field fence at Yankee Stadium!
We need a force about 4 times stronger, however I wanted to be on the low side in my estimate. All scientists know the Planck length: 10 to the -33rd Cm. I avoided using that figure, instead selecting 10 to the -36th Cm...a thousand times smaller volume. My reason is that departiculation/singularization only begins at 10 to the -33rd Cm... but is complete in the area around 10 to the -36th. Particle physicists could give us a much more exact figure to work with.
Also, cosmologically the Sun is "a small potato",.. with a diameter of 860,000 miles. Yet it is a vast, dense, particulate body with almost 20% of the mass necessary to establish the singular condition from our frame. The atomic framework of the Sun is laden with singularity (measurements go from the Suns center, although of course the mass of the Sun itself is excluded from these calculations).
Additionally, a slight increase in the selected space radius profoundly affects the volume of space selected...this must be taken into consideration.
The Suns' surrounding space out to 100 million miles is profoundly influenced, so I expected to be "on the low side" with the figures I gave David. A properly programmed computer and better Planck dimensions should be able to give more accurate results.
I have forwarded these findings to appropriate people in both the United States and in the UK.
Taken with the other simple experiments documented on this site, it can be seen that slightly modifying Schwarzschild two/ sphere geometry by replacing a point at its center with the tiny quantum Planck singular realm and applying General Relativity to the rest of the universe conceptually matches the observed universe within the limits of present observation.
A universal mass of 10 to the 60th Kg and a radius of 10 to the 40th Cm are implied.
PS: Of necessity, different quantities require different variables in the calculation of time dilation, however the two formulae are structually similar. A relationship between time, space and mass is implied...a relationship which Einstein of course asserted in proposing his theories.
The whole thing ties in with the reason light is observed as a constant from our frame, moving at 299,000Km/Sec measured to 7 or eight decimal places. Within the photonic matrix itself, light occupies the entire universe instantaneously and is related in this "white hole" configuation to the singular, inflationary, "Dark Energy" Planck Realm at the "Black Hole" antipodes.
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