Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Preliminary Study on Interplanetary Trajectory Design using Invariant Manifolds of the Circular Restricted Three Body Problem

원형 제한 3체 문제의 불변위상공간을 이용한 행성간 궤적설계 기초 연구

  • Jung, Okchul (Satellite Information Center, Korea Aerospace Research Institute) ;
  • Ahn, Sangil (Satellite Information Center, Korea Aerospace Research Institute) ;
  • Chung, Daewon (Satellite Information Center, Korea Aerospace Research Institute) ;
  • Kim, Eunkyou (Satellite Information Center, Korea Aerospace Research Institute) ;
  • Bang, Hyochoong (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology)
  • Received : 2014.09.05
  • Accepted : 2015.07.22
  • Published : 2015.08.01
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Abstract

This paper represents a trajectory design and analysis technique which uses invariant manifolds of the circular restricted three body problem. Instead of the classical patched conic method based on 2-body problem, the equation of motion and dynamical behavior of spacecraft in the circular restricted 3-body problem are introduced, and the characteristics of Lyapunov orbits near libration points and their invariant manifolds are covered in this paper. The trajectories from/to Lyapunov orbits are numerically generated with invariant manifolds in the Earth-moon system. The trajectories in the Sun-Jupiter system are also analyzed with various initial conditions in the boundary surface. These methods can be effectively applied to interplanetary trajectory designs.

본 논문에서는 원형 제한 3체 문제의 불변위상공간을 이용하여 지구-달 또는 행성간의 궤적을 설계하고 해석하는 기법을 소개한다. 2체 문제를 조합하는 고전적인 방식 대신에 원형 제한 3체 문제에 대한 운동방정식, 궤적의 동적 특성, 평형점 주변의 리아프누프 궤도와 불변위상공간의 특성을 기술한다. 원형 제한 3체 문제의 불변위상공간을 이용했을 때, 지구-달 시스템의 궤적설계 방식과 태양-목성 시스템의 경계면에서의 초기조건에 따른 궤적 특성을 수치 시뮬레이션을 통해 확인한다. 본 논문에서 제안한 원형 제한 3체 문제의 불변위상공간을 이용한 궤적설계 기법은 저추력 또는 저에너지를 이용한 달탐사 또는 행성탐사 임무 등에 활용 가능할 것이다.

Keywords

References

  1. H. Schaub, J. L Junkins, Analytical Mechanics of Space Systems, 2nd Edition, AIAA Education Series, 2009.
  2. E. Canalias et al, Assessment of mission design including utilization of libration points and weak stability boundaries, ESTEC. 2004.
  3. M. Lo, et al, "Genesis Mission Design", Proceedings of AIAA/AAS Astrodynamics Specialist Conference, AIAA 98-4468, 1998.
  4. W. S. Koon, et al, "Low Energy Transfer to the Moon", Celestial Mechanics and Dynamical Astronomy, 81, 63-73, 2001.
  5. M. Nakamiya, et al, "Preliminary Analysis of Space Transportation Systems with Spaceports Around Libration Points", AIAA Guidance, Navigation and Control Conference, AIAA 2008-6625, 2008.
  6. W. S. Koon, et al, "Constructing a Low Energy Transfer Between Jovian Moons," Contemporary Mathematics, Vol. 292, 2002.
  7. G. Gomez, et al, "Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design," American Astronautical Society, Paper 01-301, 2001.
  8. V. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies, Academic, New York. 1967.
  9. S. C. Lee, et al, "Comparison of Global Optimization Methods for Insertion Maneuver into Earth-Moon L2 Quasi-Halo Orbit Considering Collision Avoidance", International Journal of Aeronautical and Space Sciences, Vol. 15, No. 3, 2014.
  10. T. S. No, et al, "A Study on Earth-moon Transfer Orbit Design", International Journal of Aeronautical and Space Sciences, Vol. 13, No. 1, 2012.
  11. J. S. Parker and G. H. Born, "Modeling a Low-Energy Ballistic Lunar Transfer Using Dynamical Systems Theory", Journal of Spacecraft and Rockets, Vol. 45, No. 6, 2008.
  12. G. Mingotti, et al, "Optimal Low-Thrust Invariant Manifold Trajectories via Attainable Sets", Journal of Guidance, Control, and Dynamics, Vol. 34, No. 6, 2011.
  13. R. L. Anderson, and M. Lo, "Role of Invariant Manifolds in Low-Thrust Trajectory Design", Journal of Guidance, Control, and Dynamics, Vol. 32, No. 6, 2009.
  14. S. Ross and M. Lo, "The Lunar L1 Gateway: Portal to the Stars and Beyond", Proceedings of AIAA Space 2001 Conference and Exposition, AIAA 2001-4768, 2001.
  15. H. Yamato and D. B. Spencer, "Orbit Transfer via Tube Jumping in Planar Restricted Problems of Four Bodies", Journal of Spacecraft and Rockets, Vol. 42, No. 2, 2005.