Celestial dynamics and astrometry in expanding universe

TL;DR

This paper formulates the Newtonian limit of Einstein's equations within an expanding universe and derives the geodesic equations for planets and light, comparing their behaviors.

Contribution

It introduces a mathematical framework for the Newtonian limit in an expanding Friedmann universe and derives geodesic equations for celestial bodies and light.

Findings

Derived geodesic equations for planets and light in an expanding universe

Compared Newtonian and relativistic geodesics in cosmological context

Provided a mathematical formulation of Einstein's equations in Friedmann universe

Abstract

The mathematical concept of the Newtonian limit of Einstein's field equations in the expanding Friedmann universe is formulated. The geodesic equations of motion of planets and light are derived and compared.