Dong Qiao

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

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

Trajectory Design for the Transfer from the Lissajous Orbit of Sun-Earth System to Asteroids

This paper investigates the trajectory design issue for the transfer from the Lissajous orbit of CHANGE 2 probe to asteroids. First, an intersection search method, which is a general design method of low-energy transfer trajectories by searching the intersection of unstable and stable manifolds in the circular restricted three-body problem (CRTBP), is applied to produce the zero-cost flyby trajectories for the asteroid flyby missions of CHANGE 2 probe, and the simulation result shows that this method is invalid. Then, for this trajectories design issue, a perturbation method, which consists of a process of searching initial trajectories by applying velocity perturbations in the direction of unstable eigenvectors of the Lissajous orbit and a trajectory correction process with two-level differential correction, is proposed. Finally, the transfer opportunities between the Lissajous orbit of CHANGE 2 and asteroids Toutatis and 2010 JK1 are searched by the perturbation method. The results show that the method proposed in this paper can identify low-energy transfer trajectories for asteroid flyby missions of CHANGE 2. Moreover, this method provides a global understanding of the trend of impulsive maneuvers over the transfer date.

Effect of orbital shadow at an Earth-Moon Lagrange point on relay communication mission

The shadow effect is an important constraint to be considered during the implementation of exploration missions. In this paper, for the Earth-Moon Lagrange point L2 relay communication mission, shadow effect issues on a periodic orbit about L2 are investigated. A systematic analysis based on the time domain and phase space is performed including the distribution, duration, and frequency of shadows. First, the Lindstedt-Poincare and second-order differential correction methods are used in conjunction with the DE421 planetary ephemeris to achieve a mission trajectory family in a high-precision ephemeris model. Next, on the basis of a conical shadow model, the influence of different orbital phases and amplitudes on the shadow is analyzed. The distribution of the shadow is investigated as well. Finally, the configuration of the shadow and its characteristics are studied. This study provides an important reference and basis for mission orbit design and shadow avoidance for relay satellites at an Earth-Moon Lagrange point.

Design of communication relay mission for supporting lunar-farside soft landing

Chang’E-IV will be the first soft-landing and rover mission on the lunar farside. The relay satellite, which is located near the Earth-Moon L2 point for relay communication, is the key to the landing mission. Based on an analysis of the characteristics of the task and the technical difficulties associated with the relay satellite system, the overall design scheme of the relay communication mission is proposed in terms of trajectory design and communication system design among other aspects. First, according to the complex dynamic environment, a mission orbit that serves as an uninterrupted communication link is presented. A short-duration and low-energy transfer trajectory with lunar flyby is discussed. Orbital correction and a low-cost control strategy for orbit maintenance in the Earth-Moon L2 point region are provided. Second, considering the existing technical constraints, the requirement of relay communication in different stages and the design schemes of frequency division and redundant relay communication system are introduced. Finally, based on the trajectory design index and the performance of the communication system, the overall design scheme of the relay communication mission is proposed. This mission will provide the technical support and reference required for the Chang’E-IV mission.