Inverse problem, precessing orbits and autonomous forces

TL;DR

This paper explores whether a specific family of precessing orbits can be generated by autonomous force fields, extending previous work that linked certain orbits to Manev's potential, and investigates non-central force compatibility.

Contribution

It analyzes the compatibility of a different parameter choice in precessing orbits with autonomous force fields, expanding understanding beyond central force scenarios.

Findings

Previous parameter choice compatible with Manev's potential

New parameter choice not compatible with central forces

Study extends inverse problem understanding in orbital dynamics

Abstract

In the framework of the inverse problem of Dynamics we investigate the compatibility between a two-parametric family of precessing orbits and autonomous force fields. In a previous work, for a specific choice of the two parameters in the precessing family of orbits, we obtained that if the family is compatible with a central force, than this is derived from a Manev's type potential. In this work we consider another choice of the parameters in the two-parametric family of precessing orbits, for which we know that there is no central force compatible and study its compatibility with an autonomous force field.