An angular-momentum preserving dissipative model for the point-mass N -body problem

TL;DR

This paper introduces a mathematical model for the N-body problem that dissipates energy while conserving angular momentum, analyzing its effects on orbits and solution topology.

Contribution

It proposes a new dissipative model that preserves angular momentum and explores its impact on orbital dynamics and solution topology.

Findings

Forces remove energy but conserve angular momentum.

Homographic equations are equivalent to the two-body problem with dissipation.

Dissipation does not influence periapsis precession in averaged equations.

Abstract

A simple mathematical model emulating energy dissipation due to tidal effects is proposed. In this model, forces acting between masses remove energy but preserve the total angular momentum of the system. We study the effect of such forces on the particular family of orbits in central configurations, and show that a specific dependence on the mutual distances between the bodies leads to homographic equations equivalent to those of the two-body problem with dissipation. We then describe in detail the topology of solutions of the dissipative two-body system via Poincar\'e compactification. Finally, we present equations averaged over Keplerian motion showing no influence of the dissipation on periapsis precession.