Speed of Gravity




Hypothesis


The hypothesis to be explored here is that gravitational signals propagate within the ecliptic plane at a speed, cg, that is considerably slower than the speed of light. Planetary orbits in the Solar System are examined to determine if empirical evidence supports this hypothesis.

Recognizing that the sun itself has an orbital velocity in the plane of the Milky Way, and that the Milky Way has its own velocity relative to other galaxies, the principle of least action suggests that the plane of the ecliptic should be perpendicular to the velocity of the sun relative to the larger of these inertial frames. That is, a circular orbit in the ecliptic plane should trace a helical path relative to the inertial frame of interstellar space. Even a circular orbit in any other plane would require a constantly changing kinetic energy as a planet advances ahead of the sun on one side of the orbit, and falls back on the other.

Therefore, cg should not be considered to be the absolute speed of gravity through interstellar space, but rather the ecliptic component of gravitational signals radiating from the sun in the cone in which gravitational signals have a component of velocity parallel and equal to the interstellar velocity of the sun.

The sensed direction of incoming gravitational signals at an orbiting planet is along the vector sum of: cg in the direction of the instantaneous radius vector from the sun's center of gravity, and the negative of the planet's orbital velocity vector. (Positive v is the planet’s velocity relative to the sun, while negative v is the velocity of the sun's local inertial reference frame relative to the planet.)

While orbital velocities are much smaller than even the ecliptic component of the speed of gravity, the long term effects of the slight directional mismatch between the gravitational force and the instantaneous orbit radius are subtle, but profound. For example, the tangential component of the gravitational force puts a small positive torque on the orbit. This torque maximizes angular momentum, driving the geometry of planetary orbits in the ecliptic plane towards circular.

For a circular orbit, the incidence angle between incoming gravitational signals at the planet and the instantaneous radius vector from the sun is:


The magnitude of the radial component of gravitational force, (and the balancing centrifugal force), is:



Therefore, the radius of a circular orbit can be expressed as:



The above equation, applied to the eight major planets in the solar system, yields solutions consistent with the following conjectures:

1.  Planetary orbits gradually migrate to radii where orbital velocities have the following relationship to the ecliptic component of the speed of gravity: ( N is an odd integer.)



2. The ecliptic speed of gravity to be tested is given by the equation:


Empirical results for the Solar System: 

Conjecture One implies that orbit radii of the planets should comply with:



Substituting 326 km/s (conjecture two), for the speed of gravity in the above equation identifies the following integer values, N:

  N R calculated
~ km
 R
observed
~ km
 1/alpha
Mercury43 5.79e+7 5.79e+7 6.84
Venus59 1.09e+8 1.08e+7 9.39
Earth69  1.50e+8 1.50e+8 10.98
Mars85 2.28e+8 2.28e+8 13.52
Jupiter157 7.79e+8 7.78e+9 24.99
Saturn213 1.43e+9 1.43e+9 33.90
Uranus301 2.86e+9 2.87e+9 47.91
Neptune377 4.49e+9 4.50e+9 60.00



The fine structure constant is the ratio of hydrogen’s ground state electron velocity to the speed of light, and can be approximated as:


This suggests that conjecture one might be a universal property of any inverse-radius potential field.
Many physicists have considered it significant that the reciprocal of the fine structure constant is very close to the integer 137. The right column in the above table displays the reciprocal of the above approximation of alpha. (Substituting N for "861".)

Collectively, the most significant digits to the right of the decimal points (one zero, four nines, one eight, one five, and one three) represent an extremely improbable distribution with respect to Benford's law. This seems to indicate the existence of dynamic attraction basins at integer values for the reciprocal of alpha.

Conclusion:

It appears that planets in the ecliptic plane, not only migrate toward circular orbits, but also toward orbit radii where orbital velocities equal 326 km/s times the fraction: two pi over an odd integer, N. In addition, the orbits display a statistical affinity for orbits in which N is also close to an integer multiple of two pi.



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