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

Abstract:

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.

• Periodical: Applied Mechanics and Materials (Volume 390)
• Pages: 478-484
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.390.478
• Online since: August 2013
• Authors: Ya Min Wang, Dong Qiao, Ping Yuan Cui
• Keywords: Asteroid Flyby, Libration Point, Sun-Earth System, Transfer Trajectory

References

[1] E. Canalias, G. Gomez, M. Marcote, and J. J. Masdemont: Assessment of Mission Design Including Utilization of Libration Points and Weak Stability Boundaries. ESA Advanced Concept Team, (2005).

[2] R. W. Farquhar, D. P. Muhonen, and D. L. Richardson: Mission Design for a Halo Orbiter of the Earth. Journal of Spacecraft and Rockets, Vol. 14-3 (1993), pp.170-177.

DOI: 10.2514/6.1976-810

[3] R. W. Farquhar, D. P. Muhonen, C. R. Newman, and H. S. Heuberber: Trajectories and orbital maneuvers for the First Libration-Point Satellite. Journal of Guidance and Control, Vol. 3-6 (1980), pp.549-554.

DOI: 10.2514/3.56034

[4] R. W. Farquhar, and A. A. Kamel: Quasi-Periodic Orbits about the Translunar Libration Point. Celestial Mechanics, Vol. 7 (1973), pp.458-473.

DOI: 10.1007/bf01227511

[5] D. L. Richardson: Analytic Construction of Periodic Orbits about the Collinear Points. Celestial Mechanics, Vol. 22 (1980), pp.241-253.

DOI: 10.1007/bf01229511

[6] J. V. Breakwell, and J. V. Brown: The Halo, Family of 3-Dimensional Periodic Orbits in the Earth-Moon Restricted 3-Body Problem. Celestial Mechanics, Vol. 20 (1979), P. 389-404.

DOI: 10.1007/bf01230405

[7] K. C. Howell: Three-Dimensional, Periodic, Halo, orbit. Celestial Mechanics, Vol. 32-1 (1984), pp.53-71.

DOI: 10.1007/bf01358403

[8] K. C. Howell, B. Barden, and M. Lo: Application of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission. Journal of the Astronautical Sciences, Vol. 45-2 (1997), pp.161-178.

DOI: 10.1007/bf03546374

[9] G. Gomez, A. Jorba, J. J. Masdemont, and C. Simo: Study of the Transfer from the Earth to a Halo Orbit around the Equilibrium Point L1. Celestial mechanics and Dynamical Astronomy, Vol. 56-4 (1993), pp.541-562.

DOI: 10.1007/bf00696185

[10] W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross: Heteroclinic Connections Between Periodic Orbits and Resonance Transitions in Celestial Mechanics. Chaos, Vol. 10-2 (2000), pp.427-469.

DOI: 10.1063/1.166509

[11] W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross: Constructing a Low Energy Transfer Between Jovian Moons. Contemporary Mathematics, Vol. 292 (2002), pp.129-146.

DOI: 10.1090/conm/292/04919

[12] W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross: Low Energy Transfer to the Moon. Celestial Mechanics and Dynamical Astronomy, Vol. 81 (2001), pp.63-73.

DOI: 10.1023/a:1013359120468

[13] M. Lo, and S. Ross: Low Energy Interplanetary Transfers Using Invariant Manifolds of L1, L2 and Halo Orbits. AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 98-136, Feb. (1998).

[14] G. Gomez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont, S. D. Ross: Connecting Orbits and Invariant manifolds in the Spatial Restricted Three-Body Problem. Nonlinearity, Vol. 17 (2004), pp.1571-1606.

DOI: 10.1088/0951-7715/17/5/002

[15] A. F. B. A. Prado: Traveling Between the Lagrange Points and the Earth. Acta Astronautic, Vol. 39-7 (1996), pp.483-486.

[16] H. Baoyin, and R. C. Mcinnes: Trajectories to and from the Lagrange Points and the Primary Body Surfaces. Journal of Guidance, Control, and Dynamics, Vol. 29-4 (2006), pp.998-1003.

DOI: 10.2514/1.17757

[17] W. R. Wu, P. Y. Cui, D. Qiao, J. C. Huang: Design and Performance of Exploring Trajectory to Sun-Earth L2 Point for Chang'E-2 Mission (in Chinese). Chin Sci Bull (Chin Ver), Vol. 57 (2012), p.108—118.

DOI: 10.1360/972012-825