Circular orbits, Lyapunov stability and Manev-type forces

TL;DR

This paper investigates the Lyapunov stability of circular orbits in a generalized Manev two-body problem, deriving conditions for stability and comparing orbital characteristics in Newtonian and modified gravitational fields.

Contribution

It establishes Lyapunov stability for circular orbits in the Manev problem and compares orbital properties between Newtonian and Manev gravitational models.

Findings

Circular orbits exist with specific radii in the Manev problem.

Lyapunov functions confirm stability of these orbits.

Differences between Newtonian and Manev orbits are observable in real systems.

Abstract

In this article we study the stability in the sense of Lyapunov of the circular orbits in the generalized Manev two bodies problem. First, we explore the existence of the circular orbits and determine their radius. Then, using the first integrals of motion we build a positive definite function, known as a Lyapunov function. It's existence proves that the circular orbit is stable in the sense of Lyapunov. In the end, we consider several real systems of two bodies and compare the characteristics of the circular orbits in Newtonian and modified Manev gravitational field, arguing about our possibilities to observe the differences between the motion in these two fields.