Speed of Gravity

Planetary orbits in the Solar System are examined to determine if there is empirical evidence to support the hypothesis that gravitational signals propagate through inertial space at a speed, cg, that is identical to the propagation speed of deBroglie "matter waves."  It is not assumed that cg is equal to the speed of light. In fact, the evidence suggests it is much slower than light, but much faster than any of the orbital velocities.

The direction of an incoming gravitational signal, from the perspective of an orbiting planet, is the vector sum of cg in the direction of the instantaneous radius vector from the sun, and the negative of the planet's velocity vector. (Positive v is the planet’s velocity relative to inertial space, while negative v is the velocity of inertial space relative to the planet.)

While the orbital velocity is much smaller than the speed of gravity, the long term effects of this slight directional mismatch between the gravitational force and the instantaneous radius toward the sun 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, and drives the geometry of planetary orbits 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 orbit velocities have the following relationship to the speed of gravity: ( N is an odd integer.)

2. The speed of gravity is equal to the speed of deBroglie “matter waves,” and is given by the equation:

3. Planck’s constant can be expressed as:

4. The momentum of a neutron is equal to Planck’s constant divided by its deBroglie wavelength.

5. The kinetic energy of a neutron is equal to Planck’s constant multiplied by the frequency of its deBroglie wavelength.

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

The experimental value of alpha is: 0.007297351, with an uncertainty of 6 in the last decimal place. Conjecture six suggests that conjecture one might be a universal property of orbital mechanics.

Empirical results for the Solar System: 
Conjecture One implies that observed orbit radii should comply with:

Using 326 km/s (conjecture two), for the speed of gravity in the above equation identifies the following integer values, N, for the planets:
Mercury:    43
Venus:       59
Earth:        69
Mars:         85
Jupiter:    157
Saturn:    213
Uranus:   301
Neptune: 377

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