Light propagation in the field of the N-body system and the application in the TianQin mission

TL;DR

This paper develops a relativistic model for light propagation in an N-body gravitational system, incorporating velocities, accelerations, and interactions, with applications to high-precision space missions like TianQin and tests of alternative gravity theories.

Contribution

It introduces an analytical solution for light delays in a complex N-body system including interactions and deformations, advancing relativistic modeling for space observations.

Findings

Precise light delay calculations for strong gravitational fields.

Application of the model to the TianQin mission.

Potential to test alternative gravitational theories.

Abstract

Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional $N$ bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for the \emph{strong} gravitational fields, such as binary pulsars and some gravitational wave sources. The result's application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find the possible tests for the alternative gravitational theories, such as a possible determination for the post-Newtonian parameter $\gamma$ in the level of some scalar-tensor theories of gravity.