Solutions to the restricted three-body problem with variable mass

TL;DR

This paper explores specific solutions to the restricted three-body problem where bodies can gain or lose mass, extending classical solutions to cases with variable mass and analyzing their properties.

Contribution

It introduces solutions to the restricted three-body problem with variable mass, generalizing classical stationary solutions to include mass variation over time.

Findings

Analogous stationary solutions exist with variable mass

Relative distances change at the same rate over time

Additional coplanar and ring solutions are identified

Abstract

We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we find analogous solution to the five stationary solutions of the usual restricted problem of constant masses: the three collinear and the two triangular solutions, but now the relative distance of the bodies changes with time at the same rate. Under some restrictions, there are also coplanar, infinitely remote and ring solutions.