Speed of Gravity


The hypothesis to be explored here is that gravitational signals propagate 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.

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 velocity vector. (Positive v is the planet’s velocity relative to the inertial reference frame, while negative v is the velocity of the inertial reference frame relative to the planet.)

While orbital velocities are much smaller than 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 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 speed of gravity: ( N is an odd integer.)

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

3. The fine structure constant (a property of hydrogen’s ground state orbital) can be defined as:

The experimental value of alpha is 0.007297351, with an uncertainty of 6 in the last decimal place. Conjecture three suggests that conjecture one might be a universal property of any inverse-radius potential field.

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
~ km
Mercury43 5.79e+7 5.79e+7 6.92
Venus59 1.09e+8 1.08e+7 9.44
Earth69  1.50e+8 1.50e+8 11.03
Mars85 2.28e+8 2.28e+8 13.57
Jupiter157 7.79e+8 7.78e+9 25.01
Saturn213 1.43e+9 1.43e+9 33.91
Uranus301 2.86e+9 2.87e+9 47.92
Neptune377 4.49e+9 4.50e+9 60.01

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 equation for alpha from conjecture three. (Substituting N for "861".)

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

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