Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Abstract

Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps. First, a non-uniform distribution of test particles around the secondary’s orbit is obtained by fully accounting the secondary’s gravitational influence. Second, the capture efficiency is computed based on the non-uniform distribution. Several factors influencing the result are discussed. By studying the capture efficiency in the circular restricted three-body problem of different mass ratios, a power-law relation between the capture efficiency (p) and the mass ratio (μ) is established, which is given by p ≈ 0.27 × μ 0.53, within the range of 3.0035 ×10−6 ≤ μ ≤ 3.0034 × 10−5. Taking the Sun–Earth system as an example, the influence from the orbit eccentricity of the secondary on the non-uniform distribution and the capture efficiency is studied. Our studies find that the secondary’s orbit eccentricity has a negative influence on the capture efficiency.