Satellite capture mechanism in a sun-planet-binary four-body system

TL;DR

This paper investigates the binary disruption and asteroid capture mechanisms in a sun-planet-binary four-body system, deriving an analytic expression for energy exchange and validating it with numerical simulations.

Contribution

It introduces a novel analytic expression for energy exchange during binary disruption in a four-body system, validated by numerical methods, enhancing understanding of capture and escape processes.

Findings

Binary is always disrupted at orbit perigee.

Analytic and numerical energy exchange results agree within 25%.

Capture/escape regions are clearly delineated through simulations.

Abstract

This paper studies the binary disruption problem and asteroid capture mechanism in a sun-planet-binary four-body system. Firstly, the binary disruption condition is studied and the result shows that the binary is always disrupted at the perigee of their orbit instantaneously. Secondly, an analytic expression to describe the energy exchange between the binary is derived based on the instantaneous disruption hypothesis. The analytic result is validated through numerical integration. We obtain the energy exchange in encounters simultaneously by the analytic expression and numerical integration. The maximum deviation of this two results is always less than 25% and the mean deviation is about 8.69%. The analytic expression can give us an intuitive description of the energy exchange between the binary. It indicates that the energy change depends on the hyperbolic shape of the binary orbit with respect to the planet, the masses of planet and the primary member of the binary, the binary phase at perigee. We can illustrate the capture/escape processes and give the capture/escape region of the binary clearly by numerical simulation. We analyse the influence of some critical factors to the capture region finally.