The Second Post-Newtonian Light Propagation and Its Astrometric Measurement in the Solar System

TL;DR

This paper extends relativistic light propagation theories to second post-Newtonian order with new parameters, deriving equations and formulas for high-precision astrometric measurements in the solar system.

Contribution

It introduces a 2PN parameterized formalism including non-stationary fields and multipolar effects, with derived equations and gauge-invariant measurement formulas for microarcsecond accuracy.

Findings

Derived 2PN equations of motion for light propagation.

Formulated gauge-invariant angle measurement for astrometry.

Estimated effects for 1 microarcsecond precision in space missions.

Abstract

The relativistic theories of light propagation are generalized by introducing two new parameters $\varsigma$ and $\eta$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $\gamma$ and $\beta$. This new 2PN parameterized (2PPN) formalism includes the non-stationary gravitational fields and the influences of all kinds of relativistic effects. The multipolar components of gravitating bodies are taken into account as well at the first post-Newtonian order. The equations of motion and their solutions of this 2PPN light propagation problem are obtained. Started from the definition of a measurable quantity, a gauge-invariant angle between the directions of two incoming photons for a differential measurement in astrometric observation is discussed and its formula is derived. For a precision level of a few microacrsecond ($\mu$as) for space astrometry missions in the near future, we further consider a model of angular measurement, LATOR-like missions. In this case, all terms with aimed at the accuracy of $\sim1\mu$as are estimated.