Applying the theory of general relativity to reducing geodetic VLBI data

Abstract

We present an alternate formula for calculating gravitational time delay. We use this formula to reduce geodetic Very Long Baseline Interferometry (VLBI) data, taking into account gravitational effects within the solar system, and to test general relativity. The alternate formula was obtained by expanding the conventional formula in a Taylor series. We show that the gravitational delay can be split into several terms including a term due to the coordinate transformation and terms that are explicitly linked to the light deflection angle. Our formula is compared numerically with the conventional formula, and difference in arrival times within 1 ps are found at 1${}^{\circ }$ from the Sun for a full range of baseline lengths. We conclude that the standard reduction of geodetic VLBI data for the effects of general relativity is equivalent to displacing the reference radio sources from their original catalogue positions in accordance with the classical light deflection formula across the whole sky.

arXiv commentAccepted for A&A, 7 pages

References in corpus (4)

• RadioAstron -- a Telescope with a Size of 300 000 km: Main Parameters and First Observational Results
• Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
• The parallax distorsion via a weak microlensing effect
• Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission

Cited by in corpus (5)

• Finite distance corrections to the light deflection in a gravitational field with a plasma medium
• Testing General Relativity with geodetic VLBI: what profit from a single, specially designed experiment?
• Resolving VLBI correlator ambiguity in the time delay model improves precision of geodetic measurements
• Parallactic delay for geodetic VLBI and non-orthogonality of the fundamental axes
• A novel approach for the direct estimation of the instantaneous Earth rotation velocity