Time delay in the quadrupole field of a body at rest in 2PN approximation

TL;DR

This paper calculates the second post-Newtonian (2PN) quadrupole contribution to light signal delay near massive bodies like the Sun, Jupiter, and Saturn, showing its significance for high-precision measurements.

Contribution

It provides the first detailed 2PN analysis of light delay due to quadrupole fields, extending previous 1PN and 1.5PN approximations for solar system bodies.

Findings

2PN quadrupole delay up to 0.14 ps for Jupiter

1PN and 1.5PN approximations suffice for 0.001 ps accuracy

Higher multipoles like Jupiter's spin-hexapole are relevant at high precision

Abstract

The time delay of a light signal in the quadrupole field of a body at rest is determined in the second post-Newtonian (2PN) approximation in harmonic coordinates. For grazing light rays at Sun, Jupiter, and Saturn the 2PN quadrupole effect in time delay amounts up to 0.004, 0.14, and 0.04 pico-second, respectively. These values are compared with the time delay in the first post-Newtonian (1PN and 1.5PN) approximation, where it turns out that only the first eight mass-multipoles and the spin-dipole of these massive bodies are required for a given goal accuracy of 0.001 pico-second in time-delay measurements in the solar system. In addition, the spin-hexapole of Jupiter is required on that scale of accuracy.