The effect of the cosmological expansion on local systems: Post-Newtonian approximation

TL;DR

This paper investigates how the large-scale cosmological expansion influences local systems using Post-Newtonian approximation, revealing effects comparable to spacecraft anomalies and defining a critical radius where expansion effects match gravitational attraction.

Contribution

It introduces a Post-Newtonian framework to analyze cosmological expansion effects on small systems, providing new insights beyond Newtonian models.

Findings

The product Hc is approximately 7×10^-10 m/s^2, close to Pioneer spacecraft anomalies.

A new radius is derived where cosmological acceleration equals two-body gravitational attraction.

Classical critical radius is identified when the Schwarzschild radius approaches zero.

Abstract

Frequently, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach, and the General Relativity Theory is neglected. We, however, analyze the influence of cosmological expansion on small systems in the light of Post-Newtonian approximation. The equations show the product Hc=6.99*10^-10 ms^-2, and it so happens that the magnitude of this acceleration is very close the apparently anomalous acceleration of the Pioneer 10 and 11 spacecraft. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical critical radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).