Relativistic Reduction of Astrometric Observations

Abstract

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties: 1.developing theoretical conclusions only in terms of measurable quantities2.using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities3.agreement to utilize one and only one coordinate system.In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.