### Speed of Gravity

The page, Gravitational Force, demonstrates the dimensions of G/R2 to be acceleration:

$\frac{G}{R^{2}}= 3r_{e}\frac{c^{2}}{R^{2}}\left ( \frac{m_{e}}{m_{\overline{n+p}}} \right )^{4}$

Grouping the above equation into a small displacement constant and an assumed propagation speed of gravitational signals:

$\Delta r=3r_{e}\left ( \frac{m_{e}}{m_{\overline{n+p}}} \right )^{2}$

$c_{g}=c\frac{m_{e}}{m_{\overline{n+p}}}$

The acceleration felt by the masses at each end of 'R' can be written as:

$\ddot{R}_{Z}=\Delta r\left ( \frac{c_{g}}{R} \right )^{2}N$

$\ddot{R}_{N}=\Delta r\left ( \frac{c_{g}}{R} \right )^{2}Z$

The second equation can be interpreted as each quantum mass in N being displaced radially by delta-r at the rate, (cg/R)Z. Then, multiplying that displacement rate times the frequency cg/R gives the acceleration of the N mass.

Imagine Z is the number of quantum masses in the sun, and N is the quantum masses in a planet. The metaphysical question that begs asking is: How does the sun 'know' how far away the planet is, so it can adjust its displacement signal frequency to cg/R?

For the purpose of this analysis, it will be assumed that gravity incorporates the same trick used by collision avoidance transponders installed in all modern aircraft. Each transponder sends out a radio pulse in response to any pulse it receives. An aircraft receiving a pulse shortly after its pulse has been transmitted, can decode the time delay into the distance to the other aircraft:

$R=\frac{1}{2}c\Delta t$

It will be assumed that each Z quantum mass sends a delta-r displacement signal only in response to a delta-r displacement signal it receives. Further, the initial assumption of propagation speed needs to be doubled to account for the displacement signal making a round trip:

$c_{g}=2c\frac{m_{e}}{m_{\overline{n+p}}}$

Note that this does not change the displacement frequency at either end of R, since the displacement frequency sent from Z depends on the displacement frequency received from N; i.e., a 2R path.

$\frac{c_{g}}{R}=\frac{2c_{g}}{2R}$

The emerging model requires each Z quantum mass to send a return displacement signal to N at a frequency (cg/R)N, and each N quantum mass to send a return displacement signal to Z at a frequency (cg/R)Z. This model has an interesting implication for a hypothetical circular orbit. It requires that at any instant of time, the signal train from N to Z must contain exactly N displacement signals. And, of course, the reverse is true: the signal train from Z to N has exactly Z displacement signals.

For closure, each complete orbit must contain an equal number of displacement signals from each of the Z quantum masses, and each of the N quantum masses; i.e., the orbit period, 2PI R/v, must be an integer multiple of R/cg. This leads to two conjectures concerning gravitational orbits:

1. The propagation speed of gravitational signals is twice the speed of light times the electron/nucleon mass ratio.

$c_{g}=2c\frac{m_{e}}{m_{\overline{n+p}}}$

2. Gravitational orbits should migrate toward radii at which the orbit period, multiplied times the frequency, cg/R, is an integer.

$I=T\frac{c_{g}}{R}$

On the page, Gravitational Force, the relative nucleon mass (rounded to one-tenth electron mass) that yielded the best match to the published gravitational constant was 1836.9. The following table modifies this value to 1836.85 to give Jupiter an exact integer for 'I'. Since Jupiter is so massive relative to the other planets, it is least perturbed by its neighbors. Jupiter will, therefore, be assumed to be the "gold standard" for determining the speed of gravity in the solar system.

 c_g (km/s) = 326.43 m_n/m_e = 1836.85 T ~ days T ~ sec R ~ AU R ~ km I=T*c_g/R Mercury 87.97 7600608 0.387 5.79E+07 42.85 Venus 224.70 19414080 0.723 1.08E+08 58.59 Earth 365.26 31558464 1 1.50E+08 68.86 Mars 686.98 59355072 1.524 2.28E+08 84.98 Jupiter 4,332.82 374355648 5.203 7.78E+08 157.00 Saturn 10,755.70 929292480 9.539 1.43E+09 212.57 Uranus 30,687.15 2651369760 19.18 2.87E+09 301.63 Neptune 60,190.03 5200418592 30.06 4.50E+09 377.49