The role of the mass ratio in ballistic capture

ABSTRACT A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, that is, the Pluto–Charon, Earth–Moon, Sun–Jupiter, and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.

Initial Parameter Analysis about Resonant Orbits in Earth-Moon System

The initial parameters about resonant orbits in the Earth-Moon system were investigated in this study. Resonant orbits with different ratios are obtained in the two-body problem and planar circular restricted three-body problem (i.e., PCRTBP). It is found that the eccentricity and initial phase are two important initial parameters of resonant orbits that affect the closest distance between the spacecraft and the Moon. Potential resonant transition or resonant flyby may occur depending on the possibility of the spacecraft approaching the Moon. Based on an analysis of ballistic capture and flyby, the Kepler energy and the planet’s perturbed gravitational sphere are used as criteria to establish connections between the initial parameters and the possible “steady” resonant orbits. The initial parameter intervals that can cause instability of the resonant orbits in the CRTBP are obtained. Examples of resonant orbits in 1:2 and 2:1 resonances are provided to verify the proposed criteria.