1. Implication of Mass Increase From GPS Ron Hatch Natural Philosophy Alliance June 5, 2000

2. GPS in a Sun-Centered Frame (1) Show what is needed to make GPS work properly in the sun-centered isotropic light speed inertial frame. Consider clock slowing, length contraction, and mass increase with velocity. –For simplicity assume that the velocity vector of the earth’s orbit lies in one of the GPS orbital planes. This gives a velocity scale factor of:

3. GPS in a Sun-Centered Frame (2) Who cares about the length contraction of the satellite? (No one) Of the Earth? (Yes – the orbital velocity effect) But the slower clock rate has a term linear in the spin velocity. Its integral means that the clock will accumulate a bias which is peak negative (earlier) upstream and peak positive (later) downstream of earth’s velocity vector).

4. GPS in a Sun-Centered Frame (3) If velocity causes an inertial mass increase, then the satellite will increase in mass with a term due to the cross product of the orbital and spin velocities. Conservation of momentum means that it will slow down going upstream and speed up going downstream. This will cause an apparent length contraction of the orbit—the earth keeps going at the same orbital speed. The satellite orbit longitudinal contraction together with the satellite clock biases will make it look to the earth observer like the speed of light is isotropic on the earth relative to the GPS satellite.

5. GPS in a Sun-Centered Frame (4) A GRW law of kinetic force (analogous to the magnetic force) solves two inertial mass increase problems. A spin velocity kinetic force will ensure a gravitational equivalent of the Trouton-Noble null result. An orbital velocity kinetic force will lead to energy conservation of the GPS satellite orbit.