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J. Llibre, J. R. Martlnez and C. Simo, “Transversality of the Invariant Manifolds Associated to the Lyapunov Family of Periodic Orbits near L2 in the Restricted ThreeBody Problem,” Journal of Differential Equations, Vol. 58, No. 1, 1985, pp. 104-156. doi:10.1016/0022-0396(85)90024-5

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• TITLE: Transfer Trajectory Design for Mars Exploration

  AUTHORS: Jing Lü, Mingming Zhang, Qishao Lu

  KEYWORDS: Invariant Manifolds; Differential Correction Method; Lyapunov Orbit; Aerobraking; Rotating and Static Atmospheric Environments

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.3 No.2A, June 13, 2013

  ABSTRACT: With regard to the human exploration of Mars, low energy transfer trajectory is designed for Mars exploration based on the combination of invariant manifolds, differential correction and aerobraking methods. The whole transfer trajectory is composed of four stages: 1) from the Earth parking orbit to the Lyapunov orbit around Lagrange point L2 in the Sun-Earth system; 2) from the Lyapunov orbit around L2 to the Lyapunov orbit around L1 in the Sun-Mars system; 3) from the Lyapunov orbit around L1 in the Sun-Mars system to the large elliptical orbit around Mars; and 4) from the large elliptical orbit around Mars to the near-Mars parking orbit. In the first three stages, the circular restricted three-body problem is considered, and the trajectory is designed by using invariant manifolds and the differential correction method. The simulation results show that the transfer trajectory designed by means of the invariant manifolds of the Lyapunov orbit costs lower energy and shorter time of flight than that designed by means of the invariant manifold of the Halo orbit. In the fourth stage, the two-body problem is considered, and the aerobraking method is applied. A comparative performance analysis of static and rotating atmospheric models is carried out by using the details of duration, aerodynamic loading of the Mars vehicle, and other orbital parameters. It is shown that, on the low periareon where the influence of the atmospheric density increases, the changes of orbit parameters between rotating and static atmospheric environments are in large difference, such as orbital semimajor axis, orbital eccentricity, and so on. The influence of Martian rotating atmospheric environment should be considered.