Study of gravitational lunar capture in the bi-circular problem

Gravitational capture is a useful phenomenon in the design of the low energy transfer (LET) orbit for a space mission. In this paper, gravitational lunar capture based on the Sun-Earth-Moon bi-circular model (BCM) in restricted four body problem (R4BP) is studied. By the mechanics analysis in the space near the Moon, we introduce a new parameter k, the corrected ratio of the radial force, to investigate the influence of radial force on the capture eccentricity in the BCM. Then the parametric analysis is performed to detect the influences on the corrected ratio k. Considering the restriction of time-of-flight and corrected ratio, we investigate respectively the minimum capture eccentricity and the corrected minimum capture eccentricity. Via numerical analysis, we discover two special regions on the sphere of capture, in which the capture point possesses the global minimum capture eccentricity and corrected capture eccentricity. It denotes the optimal effect of the gravitational capture. In addition, the entrance points of the gravitational capture on the sphere of influence are also studied by numerical methodology. According to the results obtained, some suggestions on the design of the LET orbit are given.