Consistent Relativistic VLBI Theory with Picosecond Accuracy

The accuracy of Very Long Baseline Interferometry (VLBI), representing one of the most important space techniques of modern geodesy, especially for the determination of the Earth’s rotation parameters and baselines, is steadily increasing. Presently, delay residuals are of the order of 30 - 50 ps, corresponding to an uncertainty in length of about 1 centimeter e.g. in the determination of baselines or the position of the rotation pole. As has already been stressed by many authors, at this level of accuracy a relativistic formulation of the VLBI measuring process is indispensable (e.g. the gravitational time delay for rays getting close to the limb of the Sun amounts to 170 ns!). Starting with the work by Finkelstein et al. (1983) a series of papers has meanwhile been published on a relativistic VLBI theory (Soffelet al., 1986; Hellings, 1986; Zeller et al., 1986; Herring, 1989). However, possibly apart from Brumberg’s treatment in his new monograph (Brumberg, 1990) all of these theories have one fatal drawback: they are not based upon some consistent theory of reference frames, which relates the global, barycentric coordinates, in which the measuring process is primarily formulated and in which positions and velocities of the bodies of the solar system are computed, with the local, geocentric coordinates, comoving with the Earth, in which the geodetically meaningful baselines are defined. Furthermore, none of these theories (including Brumberg’s (1990) treatment) have the accuracy of one picosec which seems desirable with respect to the achieved residual values.