On the efficient computation of the quadrupole light deflection

Abstract

Although the formulas for the light deflection due to quadrupole gravitational field of deflecting bodies are well known, the formulas are rather complicated, so that massive computations of quadrupole light deflection (e.g., in the framework of astrometric survey missions like Gaia) are time-consuming. Considering an observer situated within a few million kilometers from the Earth (clearly the most practical case), we derive the simplest possible form of the relevant formulas still having numerical accuracy of 1 micro-arcsecond. This form leads to simple upper estimates for the quadrupole light deflection in various cases allowing one to relate the magnitude of the actual quadrupole deflection with the corresponding monopole deflection due to the same body. These upper estimates can be used to decide if, for a given configuration, the actual quadrupole deflection should be computed for a given accuracy goal.

12 pages, 0 figures, 4 tables

References in corpus (5)

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• Numerical versus analytical accuracy of the formulas for light propagation
• Influence of mass multipole moments on the deflection of a light ray by an isolated axisymmetric body
• Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles
• Light-time computations for the BepiColombo radioscience experiment