Non-Stationary Star and the Trajectory of a Circulating Test Body

TL;DR

This paper models a pulsating star's gravitational effects in flat space-time, analyzing how a test body's trajectory varies during star expansion and collapse, with potential observability in compact objects.

Contribution

It introduces a simple pulsating star model within flat space-time and derives the perturbed equations of motion for a test body, highlighting potential measurable effects.

Findings

Test body moves away during star collapse and towards during expansion

Effects are too small for Sun-Earth system to detect

Potential observability in compact, non-stationary objects

Abstract

A simple model of a spherically symmetric, pulsating star is calculated. The application to the Sun gives a 166-min radial pulsation. The theory of gravitation in flat space-time implies for a spherically symmetric, nonstationary star small time-dependent exterior gravitational effects. The perturbed equations of motion of a test body moving around the non-stationary star are given. The test body moves away from the center during the epoch of collapsing star and moves towards the center during the epoch of expanding star but the converse is also possible under some conditions. The application to the Sun-Earth system is too small to be measured. This effect may be measurable for very compact, non-stationary objects circulated of a nearby test body.