Analysis of Two-Impulse Capture Trajectories into Halo Orbits of Sun–Mars System

Abstract

T HE libration points of the three-body system attract many scientists because the libration points, natural equilibrium solutions of the circular restricted three-body problem (CRTBP), offer the unique possibility to have space astronomical observation [1] and low-energy interplanetary transfer [2–7]. Moreover, the libration points will be considered as a candidate location to establish a reusable and repetitive interplanetary cargo system or transportation system in the future [8–11]. When constructing a spaceport in the vicinity of libration points in a sun–planet system, the design and analysis of spacecraft escape and capture trajectories from or to halo orbits around the libration points, such as L1 or L2 point, is an important problem for interplanetary transportation systems and have been a topic of study. Recently, Nakamiya et al. [10,11] studied the escape and capture trajectories from or to halo orbits around the L1 or L2 points using impulsive maneuvers at periapsis of the manifolds for interplanetary transfers. In particular, a systematic analysis of capture trajectories to Lyapunov/halo orbits from interplanetary trajectories in the Hill three-body problem was carried out [10]. When searching the first four periapsis passage points of stable manifolds, the periapsis altitude of 200 km, with respect to Mars, was considered. It is known that these stable manifolds would play a key role in the searching process of capture trajectories. Moreover, in previous research, little attention has been given to some branches of stable manifolds that have only one opportunity of Mars flyby and periapsis altitude is larger than 200 km. These branches would provide some unique capture opportunities for interplanetary transfer missions. Therefore, the aim of this Note is to analyze the two-impulse capture trajectories into halo orbits of the sun–Mars system by adopting these discarded branches of stable manifolds. This Note is organized as follows. Section II briefly describes the problem. Section III defines the parameters of two-impulse capture trajectories and presents the numerical analysis method. Section IV applies our study of capture trajectories to halo orbits to a sun–Mars system. Some novel capture opportunities are found. II. Brief Description of the Problem