Efficient computation of the quadrupole light deflection

TL;DR

This paper presents optimized formulas and criteria for efficiently computing quadrupole light deflection in the Gaia relativity model, improving performance and accuracy for astronomical observations of quasars and solar system objects.

Contribution

It introduces simplified formulas and a priori criteria for quadrupole light deflection calculations within the Gaia model, enhancing computational efficiency and accuracy.

Findings

Simplified quadrupole deflection formulas for Gaia's orbit and parameters.

A priori criteria to determine when to compute quadrupole deflection.

Upper bounds for quadrupole Shapiro effect on solar system objects.

Abstract

Efficient computation of the quadrupole light deflection for quasars/quasars and solar system objects within the framework of the baseline Gaia relativity model (GREM) is discussed. Two refinements have been achieved with the goal to improve the performance of the model: First, the quadrupole deflection formulas for both cases are simplified as much as possible considering the Gaia nominal orbit (only approximate minimal distances between Gaia and the giant planets were used here), physical parameters of the giant planets and the envisaged accuracy of 1 microarcsecond for individual systematic effects. The recommended formulas are given by Eq.(40) for stars/quasars and by Eq.(81) for solar system objects. Second, simple expressions for the upper estimate of the quadrupole light deflection have been found allowing, with a few additional arithmetical operations, to judge a priori if the quadrupole light deflection should be computed or not for a given source and for a given requested accuracy. The recommended criteria are given by Eq.(45) for stars/quasars and by Eq.(92) for solar system objects. Additionally, the quadrupole Shapiro effect for solar system objects is reconsidered. A strict upper bound of quadrupole Shapiro effect for solar system objects is given in Eq.(109).