On the effect of the central body small deformations on its satellite trajectory in the problem of the two-body gravitational interaction

TL;DR

This paper investigates how small deformations of a central body's shape affect the trajectory of its satellite in a two-body gravitational system, using numerical solutions based on classical mechanics.

Contribution

It introduces a numerical approach to analyze the impact of central body deformations on satellite trajectories, linking gravity anomalies to orbital discrepancies.

Findings

Angular discrepancy correlates with gravity anomalies.

Deformations significantly influence satellite pericenter positions.

Abstract

The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point (satellite). The relationship of the angular discrepancy between the calculated and actual positions of the satellite pericenter with central body's gravity anomaly has been established.