Ground-based VLBI relativistic time delay model of solar system objects

A relativistic time delay model for ground-based VLBI observations of solar system objects is derived first in the barycentric reference system of the solar system, and then transformed to the non-spinning geocentric reference system. A universal analytic expression is presented, from which the model given by Pin Jin-song can be obtained. It is also pointed out that the several models for extragalactic source observations, such as those proposed by Zhu & Groten, Shapiro and those recommended by IERS(92, 96), can be derived from this formula if the geocentric distance of the source is taken to be infinite. This formula is recommended for practical applications because it is rigorously analytic and errorless. The range of application of the derived formula and the estimation of the size of various neglected terms, as well as the calculation procedures of the model are discussed in detail.