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

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 these 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 analyze the influence of some critical factors to the capture region finally.