Possible effects of anisotropy ofG on celestial orbits |
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Authors: | John P Vinti |
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Institution: | (1) MIT Measurement Systems Laboratory, Cambridge, Mass., USA |
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Abstract: | Will (1971) has discussed a possible anisotropy in the gravitational constantG. Suppose that the attractive gravitational force between two particles of massesm
1 andm
2 is given by the usual expressionF=–Gm
1
m
2
r/r
3, wherer is the separation vector. Ifc is the velocity of light in vacuo and if 1
r
r/r, he expresses the anisotropy byG=G
1+ (v·1
r/c)2], whereG
is a constant,v is identified practically as the velocity of the Sun around the galaxy, and ![epsi](/content/h72j05l56051p257/xxlarge949.gif) 1. Will's suggestion is to look for such an effect in the laboratory.The purpose of the present paper is to look for such an effect in the solar system, wherem
1 andm
2 become the masses of the Sun and a planet or of the Earth and the Moon. For simplicity I consider only those planets whose orbits are close to the ecliptic, so that the angle betweenv and the plane of the ecliptic is about 59°.With the above force, the resulting two-body problem is completely solvable. The results are these. If =1, there is an increase in mean motion of 7 parts in 108, a periodic fluctuation in true longitude with period half that of the orbit and amplitude ranging possibly from 0.01 to 0.02 , and periodic fluctuations in the radius vector, with period also one half that for the orbit. The amplitudes are: 2.7 km for Mercury, 5.1 km for Venus, 7.0 km for Mars, 18 m for the Moon about the Earth, and 28 cm for a close artificial satellite with inclination 23°. The more conservative estimate <0.0115 would reduce these values by the factor 70. |
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Keywords: | |
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