`Similar' coordinate systems and the Roche geometry. Application

TL;DR

This paper introduces a new 'similarity' relation in the restricted three-body problem, leading to 'similar' trajectories and coordinate systems that simplify analytical relations in Roche geometry, with applications demonstrated through existing astrophysical relations.

Contribution

It presents a novel 'similarity' relation and coordinate systems that enhance understanding and analytical derivations in Roche geometry within the restricted three-body problem.

Findings

Derivation of new 'similar' trajectories.

Simplified analytical relations in Roche geometry.

Application of the method to existing astrophysical results.

Abstract

A new equivalence relation, named relation of 'similarity' is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named 'similar' trajectories) are obtained; they have the theoretical role to give us new details in the restricted three-body problem. The 'similar' coordinate systems allow us in addition to obtain a unitary and an elegant demonstration of some analytical relations in the Roche geometry. As an example, some analytical relations published in Astrophysical Journal by Seidov in 2004 are demonstrated.