Astronomical relativistic reference systems with multipolar expansion: the global one

TL;DR

This paper develops a multipolar expansion of the global solar system relativistic reference system, explicitly expressing post-Newtonian mass and spin moments to improve modeling and interpretation of high-precision astronomical data.

Contribution

It introduces a multipolar expansion of the global relativistic reference system with explicit post-Newtonian moments, enhancing data analysis accuracy.

Findings

Explicit expression of post-Newtonian mass and spin moments in the metric.

Full expression of the global relativistic metric provided.

Facilitates modeling of observations and experiments.

Abstract

With rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories of astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems. This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As the first step, the global solar system reference system is multipolarly expanded and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.