Constraints on Bounded Motion and Mutual Escape for the Full 3-Body Problem

TL;DR

This paper extends the analysis of gravitational fission and escape dynamics from the 2-body to the 3-body problem, deriving new mass ejection limits and stability criteria for three-body systems.

Contribution

It provides the first rigorous limits on mass ejection and escape in the full 3-body problem, expanding understanding of asteroid fission and reconfiguration.

Findings

The 3-body system can eject up to 0.31 of the total mass, more than the 0.17 limit in the 2-body case.

Derived strict conditions for component escape and stable equilibrium configurations.

Focused on the Spherical Full Three Body Problem to obtain these results.

Abstract

When gravitational aggregates are spun to fission they can undergo complex dynamical evolution, including escape and reconfiguration. Previous work has shown that a simple analysis of the full 2-body problem provides physically relevant insights for whether a fissioned system can lead to escape of the components and the creation of asteroid pairs. In this paper we extend the analysis to the full 3-body problem, utilizing recent advances in the understanding of fission mechanics of these systems. Specifically, we find that the full 3-body problem can eject a body with as much as 0.31 of the total system mass, significantly larger than the 0.17 mass limit previously calculated for the full 2-body problem. This paper derives rigorous limits on a fissioned 3-body system with regards to whether fissioned system components can physically escape from each other and what other stable relative equilibria they could settle in. We explore this question with a narrow focus on the Spherical Full Three Body Problem studied in detail earlier.