Light-propagation in the gravitational field of moving quadrupoles

TL;DR

This paper confirms that for accurate light-deflection calculations in Gaia data reduction, the positions of moving planets should be evaluated at retarded time, aligning with previous simplified formulas and improving modeling of gravitational effects.

Contribution

The paper demonstrates that a simplified quadrupole light-deflection formula aligns with previous solutions, confirming the necessity of using retarded positions of moving planets.

Findings

Simplified formula matches previous solutions

Retarded positions are essential for accurate modeling

Improves Gaia data reduction accuracy

Abstract

A simplified formula for light-deflection in the quadrupole field of moving massive bodies has been obtained in [1,2,3], which will be applied for Gaia data reduction. So far, in Gaia data reduction it has been assumed that the positions of the giant planets should be computed at the retarded instant of time. The problem of light-deflection due to quadrupole field of moving planets has been re-considered in [4]. According to their solution, the position and velocity of the massive body have to be taken at retarded time. We show that the solution given in [4] coincides with our simplified quadrupole formula obtained in [1,2,3]. This coincidence implies that the positions of giant planets have, in fact, to be taken at retarded time.