Orbit determination in the relativistic geocentric reference frame

The results obtained using a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-Earth satellites should be equivalent to some limiting accuracy. The purpose of this paper is to present the model for the effects of relativity when processing satellite laser range data in the geocentric frame and to demonstrate the equivalence of the results to those obtained using the barycentric model through the analysis of three years of laser tracking data taken for the LAGEOS satellite. It is shown that the simpler formulation in the geocentric frame is adequate for the purpose of satellite orbit determination. A correction to the conventional barycentric equations of motion is also shown to be required.