Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference

Abstract

In order to obtain accurate computed values of Earth-based range and Doppler observables of a beep space probe, an expression is required for the time differencet−τ, wheret is coordinate time in the solar system barycentric space-time frame of reference and τ is proper time recorded on a fixed atomic clock on earth. This paper is part 1 of a two-part article which obtains an expression fort−τ which is suitable for use in obtaining computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in the computation of Very Long Baseline Interferometry data types. Part 1 obtains an expression fort−τ which is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on Earth which reads τ. In Part 2, this expression will be transformed to a function of time and the Earth-fixed coordinates of the atomic clock.