Relativistic Gravitational Effects of the Central Mass Object on Orbiting Systems around that Central Mass Object
Keywords: GPS, Relativity, Gravitation, Clocks,Time, Noon-Midnight
Clocks in the vicinity of earth as observed by GPS (Global Positioning System), do not seem to vary with their distance from the sun. This phenomenon has been described as the "noon-midnight" problem and was discussed by Hatch (2004). Clocks on the earth or in orbit around the earth are closer to the sun at noon than at midnight, however, the difference in gravitational potential from the sun does not result in different clock rates. The relativistic gravitational forces in the throughout (???) the near earth system are very nearly the same as at the orbital radius. This paper is a detailed analysis which shows that the observations are a result of relativistic equivalence and that the change in distance effects are nearly canceled by the corresponding change in orbital velocity. Previous authors have suggested that the solution to the problem is the equivalence principle but, to my knowledge, no thorough mathematical analysis has been presented.