Abstract
The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.
Similar content being viewed by others
References
Andreu, M. A.: 1998, 'The Quasi-bicircular problem', Thesis, Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona.
Andreu, M. A.: 2002, 'Dynamics in the center manifold around L2 in the quasi-bicircular problem', Celest. Mech. & Dyn. Astr. 84, 105-133.
Andreu, M. A. and Simó, C.: 1999a, 'Translunar Halo orbits in the quasi-bicircular problem', B. A. Steves and A. E. Roy (eds), The Dynamics of Small Bodies in the Solar System, NATO ASI, 1997, Maratea, Italy, pp. 309-314.
Andreu, M. A. and Simó, C.: 1999b, 'Estudio de la estabilidad de una familia de toros 2D del problema Cuasibicircular, XVI CEDYA/VI CMA Vol. I, 1999, Las Palmas de Gran Canaria, Spain, pp. 131-138.
Belbruno, E. A. and Miller, J. K.: 1993, 'Sun perturbed Earth to Moon transfers with ballistic capture', J. Guidance Cont. Dyn. 16, 770-775.
Castellà, E. and Jorba, À.: 2000, 'On the vertical families of two-dimensional tori near the triangular points of the bicircular problem', Celest. Mech. & Dyn. Astr. 76(1), 35-54.
Farquhar, R. W.: 1970, The Control and Use of Libration-Point Satellites, NASA TR R346.
Farquhar, R.W. and Kamel, A. A.: 1973, 'Quasi-periodic orbits about the translunar libration point', Celest. Mech. & Dyn. Astr. 7, 458-473.
Gómez, G., Llibre, J., Martínez, R. and Simó, C.: 1985, Station keeping of libration point orbits, ESOC contract 5648/83/D/JS(SC), Final Report.
Gómez, G., Llibre, J., Martínez, R. and Simó, C.: 1987, Study on orbits near the triangular libration points in the perturbed restricted three body problem, ESOC contract 6139/84/D/JS(SC), Final Report.
Gómez, G., Jorba, À., Masdemont, J. and Simó, C.: 1991, Study refinement of semianalytical halo orbit theory, ESOC contract 8625/89/D/MD(SC), Final Report.
Gómez, G., Jorba, À., Masdemont, J. and Simó, C.: 1993, Study of Poincaré maps for orbits near Lagrangian points, ESOC contract 9711/91/D/IM(SC), Final Report.
Gómez, G., Masdemont, J. and Simó, C.:1998, 'Quasihalo orbits associated with libration points', J. Astronautical Sci. 46.
Gómez, G., Koon, W. S., Lo,.W., Marsden,. E., Masdemont, J. and Ross,. D.: 2001a, Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design, Astrodynamics Specialist Meeting, Quebec City, Canada, AAS01-31.
Gómez, G., Mondelo, J. M. and Simó, C.: 2001b, Refined Fourier analysis: procedures, error estimates and applications, Preprint.
Gutzwiller, M. C.: 1998, 'Moon-Earth-Sun: the oldest three-body problem', Rev. Mod. Phys. 70(2).
Howell, K. C., Barden, B. T., Wilson, R. S. and Lo, M. W.: 1997, Trajectory Design Using a Dynamical Systems Approach with Application to Genesis, AAS/AIAA Astrodymics Specialist Conference, AAS Paper 97-709.
Huang, S. S.: 1960, Very restricted four body problem, NASA Technical Note D-501.
Jorba, À.: 2000, On practical stability regions for the motion of a small particle close to the equilateral points of the real Earth-Moon system, In: J. Delgado, E. A. Lacomba, E. Pérez-Chavela and J. Llibre (eds), Hamiltonian Systems and Celestial Mechanics, World Scientific Monograph Series in Mathematics, Vol.6, pp. 197-213, Singapore.
Jorba, À. and Villanueva, J.: 1997, 'On the persistence of lower dimensional invariant tori under quasi-periodic perturbations', J. Nonlinear Sci. 7, 427-473.
Koon, W. S., Lo, M. W., Marsden, J. E. and Ross, S. D.: 1999, 'The genesis trajectory and heteroclinic connections', AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, AAS99-451.
Koon, W. S., Lo, M. W., Marsden, J. E. and Ross, S. D.: 2001, 'Low energy transfer to the Moon', Celest. Mech. & Dyn. Astr. 81, 63-73.
Laskar, J., Froeschlé, C. and Celletti, A.: 1992, 'The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping', Physica D 56, 253-269.
Simó, C.: 1998, 'Effective computations in celestial mechanics and astrodynamics'. In: V. Rumyantsev and A. Karapetyan (eds), Modern Methods of Analytical Mechanics and Their Applications, CISM Courses and Lectures, Vol. 387, Springer, Berlin.
Stoer, J. and Bulirsch, R.: 1980, Introduction to Numerical Analysis, Springer-Verlag, Berlin.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.
Wiesel, W.: 1984, The restricted Earth-Sun-Moon problem I: Dynamics and libration point orbits, Dept. Aeron. and Astron., Air Force Institute of Technology Wright-Patterson AFB, Ohio.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andreu, M.A. Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System. Celestial Mechanics and Dynamical Astronomy 86, 107–130 (2003). https://doi.org/10.1023/A:1024178901666
Issue Date:
DOI: https://doi.org/10.1023/A:1024178901666