[Ivan (Ivan)]

Will this work? As we know, the speed of gravity is known to be equal to the speed of light. The following experiment could provide a reasonably accurate result.


Let’s say we place a satellite at the Lagrangian point L4 at t=0, see diagram. The satellite’s on-board clock is synchronised to the Earth’s clock. At t=0 the satellite would, in a gravitational sense, “see” the Earth at point P0, as gravity would take a finite time (approx 500 seconds) to reach the satellite. At t=0 the Earth would, in fact, be at point P1, or approximately 450.5 light seconds from the satellite, since the Earth would have moved to P1 500 seconds ago.
If we launched a time-stamped radio signal from the satellite at t=0 towards Earth, it would take approximately 401 seconds (99 second difference) for this signal to reach Earth, since the Earth has now moved from point P1 to point P2.

The above calculations assumes the speed of gravity is equal to the speed of light. If the speed of gravity was different, there would be a different delta in the time that the pulse reaches the Earth. In the scenario where the speed of gravity is infinite, we would only measure approximately a 45 second difference, as the satellite would experience an “instant” gravitational effect (t=0 is now at P0) from the Earth and we would be measuring just the finite speed of light.

Does relativity effect the calculations? I feel it would be insignificant. Have I made some gross assumptions? Are the calculations correct? Appreciate your comments.