Relativistic reference systems and motion of test bodies in the vicinity of the earth

Abstract

Relativistic theory of constructing nonrotating harmonic reference systems (RS) is developed. The theory enables one to produce the celestial RS for solar-system dynamics neglecting the gravitational field of the Galaxy. Particular attention is focused on the barycentric RS (BRS) with the origin at the solar-system barycentre and the geocentric RS (GRS) with the origin at the geocentre. It is assumed therewith that the velocities of bodies are small as compared with the light velocity and the gravitational field is weak everywhere. The specific RS and the gravitational field are described by the metric tensor to be found by Newtonian approximations from the Einstein field equations with given boundary conditions. The BRS coordinates cover all the solar-system space. The GRS coordinates are initially restricted in space by the orbit of the Moon. The relationship between BRS and GRS is established by the asymptotic matching technique. The explicit transformation formulae permit to prolonge the GRS coordinates beyond the lunar orbit to cover actually all the solar-system space. The GRS equations of the Earth satellite motion have been deduced. The relativistic right-hand members of these equations contain Schwarzschild, Lense-Thirring and quadrupole terrestrial perturbations as well as tidal perturbations due to the Sun, the Moon and the major planets. The equations are derived by two different techniques. The first one implies the application of the geodesic principle to the GRS metric. The second one is based on the transformation of the BRS satellite equations of motion into the GRS equations. Both techniques result in the same final expressions.