Transfer Trajectory Design for Mars Exploration

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 *L**L*2 to the Lyapunov orbit around *L**L*

Cite this paper

J. Lü, M. Zhang and Q. Lu, "Transfer Trajectory Design for Mars Exploration,"*International Journal of Astronomy and Astrophysics*, Vol. 3 No. 2, 2013, pp. 5-16. doi: 10.4236/ijaa.2013.32A002.

J. Lü, M. Zhang and Q. Lu, "Transfer Trajectory Design for Mars Exploration,"

References

[1] J. Barrow-Green, “Poincare and the Three-Body Problem,” American Mathematical Society-London Mathematicl Society, Providence, 1997.

[2] B. Wie, “Space Vehicle Dynamic and Control,” American Institute of Aeronautics and Astronautics, Reston, 1998.

[3] R. W. Farquhar, “The Flight of ISEE-3/ICE: Origns, Mission History, and a Legacy,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Boston, 10-12 August 1998, pp. 98-4464.

[4] P. Sharer and T. Harrington, “Trajectory Optimization for the ACE Halo Orbit Mission,” AAS/AIAA Astrodynamics Specialist Conference, San Diego, 29-31 July 1996, pp. 96-3601.

[5] P. Sharer and D. Folta, “Wind Extended Mission Design,” AAS/AIAA Astrodynamics Conference, San Diego, 29-31 July 1996, pp. 96-3640.

[6] H. Franz, P. Sharer, K. Ogilvie and M. Desch, “Wind Nominal Mission Performance and Extended Mission Design,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Boston, 10-12 August 1998, pp. 98-4467.

[7] O. O. Cuevs, L. Kraft-Newman, M. A. Mesarch and M. Woodard, “An Overview,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Monterey, 5-8 August 2002, pp. 2002-4425.

[8] M. A. Mesarch, D. Rohrbaugh and C. Schiff, “Contingency Planning for the Microwave Anisotropy Probe Mission,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Monterey, 5-8 August 2002, pp. 2002-4426.

[9] S. Stalos, D. Folta, B. Short, J. Jen and A. Seacord, “Optimum Transfer to Largeamplitude Halo Orbit for the Solar and Heliospheric Observatory,” AAS/GSFC International Symposium on Space Flight Dynamics, Greenbelt, 26-30 April 1993, pp. 93-553.

[10] W. S. Koon, M. W. Lo, J. E. Marsden and S. D. Ross, “Dynamical Systems, the Three-Body Problem, and Space Mission Design,” Springer, Berlin, 2007.

[11] M. W. Lo, “The Interplanetary Superhighway and the Origins Program,” IEEE Aerospace 2002 Conference, Big Sky, 9-16 March 2002, pp. 3543-3562.

[12] W. S. Koon, W. Martin, M. W. Lo, J. E. Marsden and S. D. Ross, “Shoot the Moon,” AAS/AIAA Astrodynamics Specialist Conference, Clearwater, 2000, pp. 100-167.

[13] 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, No. 1-2, 2001, pp. 63-73. doi:10.1023/A:1013359120468

[14] G. Gomez, W. S. Koon, M. W. Lo, J. E. Marsden and J. J. Masdemont, “Connecting Orbits and Invariant Manifold in the Spatial Restricted Three-Body Problem,” Nonlinearity, Vol. 17, No. 5, 2004, pp. 1571-1606. doi:10.1088/0951-7715/17/5/002

[15] K. C. Howell, D. L. Mains and B. T. Barden, “Transfer Trajectories from Earth Parking Orbits to Sun-Earth Halo Orbits,” AAS/AIAA Spaceflight Mechanics Meeting, Cocoa Beach, 14-16 February 1994, pp. 94-160.

[16] E. A. Belbruno and J. K. Miller, “Sun-Peturbed Earth-toMoon Transfers with Ballistic Capture,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 4, 1993, pp. 770-775. doi:10.2514/3.21079

[17] G. P. Alonso, “The Design of System-to-System Transfer Arcs Using Invariant Manifolds in the Multi-Body Problem,” Ph.D. Dissertation, Purdue University, West Lafayette, 2006.

[18] F. Topputo, M. Vasile and A. E. Finzi, “Combining Two and Three-Body Dynamics for Low Energy Transfer Trajectories of Practical Interest,” Proceedings of the 55th International Astronautical Congress, Vancouver, 4-8 October 2004, pp. 584-596.

[19] M. Xu and S. J. Xu, “Stability Analysis and Transiting Trajectory Design for Retrograde Orbits around Moon,” Journal of Astronautics, Vol. 30, No. 5, 2009, pp. 1785-1791.

[20] M. J. Capinski, “Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun Planar Restricted Circular Three-Body Problem,” 2011. http://arxiv.org/pdf/ 1109.1439v2.pdf

[21] 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

[22] H. X. Baoyin and C. R. McInnes, “Trajectories to and from the Lagrange Points and the Primary Body Surfaces,” Journal of Guidance, Control and Dynamics, Vol. 29, No. 4, 2006, pp. 998-1003. doi:10.2514/1.17757

[23] S. P. Gong, J. F. Li and H. X. Baoyin, “Lunar Landing Trajectory Design Based on Invariant Manifold,” Applied Mathematics and Mechanics, Vol. 28, No. 2, 2007, pp. 201-207. doi:10.1007/s10483-007-0208-1

[24] X. Min, T. Pan and H. Guo, “Analysis of Orbit Capture Method for Mars Vehicle,” Spacecraft Engineering, Vol. 17, No. 6, 2008, pp. 39-43.

[25] F. Xiao, “Man-Made Earth Satellite Orbit Perturbation Theory,” Press of National University of Defense Technology, Changsha, 1995, pp. 178-192.

[26] Kh. I. Khalil, “The Drag Exerted by an Oblate Rotating Atmosphere on an Artifical Satellite,” Applied Mathematics and Mechanics, Vol. 23, No. 9, 2002, pp. 903-915. doi:10.1007/BF02437712

[27] D. L. Richardson, “Periodic Orbits about the L1 and L2 Collinear Points in the Circular-Restricted Problem,” Computer Sciences Corporation, Technical Report, 1978.

[28] K. C. Howell, B. T. Barden and M. W. Lo, “Application of Dynamical Systems Theory to Trajectory Design for a Lagrange Point Mission,” Journal of Astronautical Sciences, Vol. 45, No. 1, 1997, pp. 161-178.

[29] K. C. Howell, B. T. Barden, R. S. Wilson, et al., “Trajectory Design Using a Dynamical Systems Approach with Application to Genesis,” AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, 4-7 August 1997, pp. 68-178.

[1] J. Barrow-Green, “Poincare and the Three-Body Problem,” American Mathematical Society-London Mathematicl Society, Providence, 1997.

[2] B. Wie, “Space Vehicle Dynamic and Control,” American Institute of Aeronautics and Astronautics, Reston, 1998.

[3] R. W. Farquhar, “The Flight of ISEE-3/ICE: Origns, Mission History, and a Legacy,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Boston, 10-12 August 1998, pp. 98-4464.

[4] P. Sharer and T. Harrington, “Trajectory Optimization for the ACE Halo Orbit Mission,” AAS/AIAA Astrodynamics Specialist Conference, San Diego, 29-31 July 1996, pp. 96-3601.

[5] P. Sharer and D. Folta, “Wind Extended Mission Design,” AAS/AIAA Astrodynamics Conference, San Diego, 29-31 July 1996, pp. 96-3640.

[6] H. Franz, P. Sharer, K. Ogilvie and M. Desch, “Wind Nominal Mission Performance and Extended Mission Design,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Boston, 10-12 August 1998, pp. 98-4467.

[7] O. O. Cuevs, L. Kraft-Newman, M. A. Mesarch and M. Woodard, “An Overview,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Monterey, 5-8 August 2002, pp. 2002-4425.

[8] M. A. Mesarch, D. Rohrbaugh and C. Schiff, “Contingency Planning for the Microwave Anisotropy Probe Mission,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, Monterey, 5-8 August 2002, pp. 2002-4426.

[9] S. Stalos, D. Folta, B. Short, J. Jen and A. Seacord, “Optimum Transfer to Largeamplitude Halo Orbit for the Solar and Heliospheric Observatory,” AAS/GSFC International Symposium on Space Flight Dynamics, Greenbelt, 26-30 April 1993, pp. 93-553.

[10] W. S. Koon, M. W. Lo, J. E. Marsden and S. D. Ross, “Dynamical Systems, the Three-Body Problem, and Space Mission Design,” Springer, Berlin, 2007.

[11] M. W. Lo, “The Interplanetary Superhighway and the Origins Program,” IEEE Aerospace 2002 Conference, Big Sky, 9-16 March 2002, pp. 3543-3562.

[12] W. S. Koon, W. Martin, M. W. Lo, J. E. Marsden and S. D. Ross, “Shoot the Moon,” AAS/AIAA Astrodynamics Specialist Conference, Clearwater, 2000, pp. 100-167.

[13] 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, No. 1-2, 2001, pp. 63-73. doi:10.1023/A:1013359120468

[14] G. Gomez, W. S. Koon, M. W. Lo, J. E. Marsden and J. J. Masdemont, “Connecting Orbits and Invariant Manifold in the Spatial Restricted Three-Body Problem,” Nonlinearity, Vol. 17, No. 5, 2004, pp. 1571-1606. doi:10.1088/0951-7715/17/5/002

[15] K. C. Howell, D. L. Mains and B. T. Barden, “Transfer Trajectories from Earth Parking Orbits to Sun-Earth Halo Orbits,” AAS/AIAA Spaceflight Mechanics Meeting, Cocoa Beach, 14-16 February 1994, pp. 94-160.

[16] E. A. Belbruno and J. K. Miller, “Sun-Peturbed Earth-toMoon Transfers with Ballistic Capture,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 4, 1993, pp. 770-775. doi:10.2514/3.21079

[17] G. P. Alonso, “The Design of System-to-System Transfer Arcs Using Invariant Manifolds in the Multi-Body Problem,” Ph.D. Dissertation, Purdue University, West Lafayette, 2006.

[18] F. Topputo, M. Vasile and A. E. Finzi, “Combining Two and Three-Body Dynamics for Low Energy Transfer Trajectories of Practical Interest,” Proceedings of the 55th International Astronautical Congress, Vancouver, 4-8 October 2004, pp. 584-596.

[19] M. Xu and S. J. Xu, “Stability Analysis and Transiting Trajectory Design for Retrograde Orbits around Moon,” Journal of Astronautics, Vol. 30, No. 5, 2009, pp. 1785-1791.

[20] M. J. Capinski, “Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun Planar Restricted Circular Three-Body Problem,” 2011. http://arxiv.org/pdf/ 1109.1439v2.pdf

[21] 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

[22] H. X. Baoyin and C. R. McInnes, “Trajectories to and from the Lagrange Points and the Primary Body Surfaces,” Journal of Guidance, Control and Dynamics, Vol. 29, No. 4, 2006, pp. 998-1003. doi:10.2514/1.17757

[23] S. P. Gong, J. F. Li and H. X. Baoyin, “Lunar Landing Trajectory Design Based on Invariant Manifold,” Applied Mathematics and Mechanics, Vol. 28, No. 2, 2007, pp. 201-207. doi:10.1007/s10483-007-0208-1

[24] X. Min, T. Pan and H. Guo, “Analysis of Orbit Capture Method for Mars Vehicle,” Spacecraft Engineering, Vol. 17, No. 6, 2008, pp. 39-43.

[25] F. Xiao, “Man-Made Earth Satellite Orbit Perturbation Theory,” Press of National University of Defense Technology, Changsha, 1995, pp. 178-192.

[26] Kh. I. Khalil, “The Drag Exerted by an Oblate Rotating Atmosphere on an Artifical Satellite,” Applied Mathematics and Mechanics, Vol. 23, No. 9, 2002, pp. 903-915. doi:10.1007/BF02437712

[27] D. L. Richardson, “Periodic Orbits about the L1 and L2 Collinear Points in the Circular-Restricted Problem,” Computer Sciences Corporation, Technical Report, 1978.

[28] K. C. Howell, B. T. Barden and M. W. Lo, “Application of Dynamical Systems Theory to Trajectory Design for a Lagrange Point Mission,” Journal of Astronautical Sciences, Vol. 45, No. 1, 1997, pp. 161-178.

[29] K. C. Howell, B. T. Barden, R. S. Wilson, et al., “Trajectory Design Using a Dynamical Systems Approach with Application to Genesis,” AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, 4-7 August 1997, pp. 68-178.