Abstract
We study numerically the asymptotic homoclinic and heteroclinic orbits around the hyperbolic Lyapunov periodic orbits which emanate from Euler's critical points L 1 and L 2, in the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these Lyapunov orbits, are also presented. Poincaré surface of sections of these manifolds on appropriate planes and several homoclinic and heteroclinic orbits for the gravitational case as well as for varying radiation factor q 1, are displayed. Homoclinic-homoclinic and homoclinic-heteroclinic-homoclinic chains which link the interior with the exterior Hill's regions, are illustrated. We adopt the Sun-Jupiter system and assume that only the larger primary radiates. It is found that for small deviations of its value from the gravitational case (q 1 = 1), the radiation pressure exerts a significant impact on the Hill's regions and on these asymptotic orbits.
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References
Chernicov, Yu. A.: 1970, Soviet Astron. 14, 176.
Conley, C.: 1968, SIAM J. Appl. Math. 16, 732.
Deprit, A. and Henrard, J.: 1965, Astron. J. 70, 271.
Deprit, A. and Henrard, J.: 1969, Astron. J. 74, 308.
Gómez, G., Llibre, J. and Masdemont, J.: 1988, Celestial Mechanics 44, 239.
Gómez, G., Koon, W.S., Lo, M.W., Marsden, J.E., Masdemont, J. and Ross, S.D.: 2004, Nonlinearity 17, 1571.
Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S.D.: 1999, AAS/AIAA Astrodynamics Specialist Conf. (Girdwood, Alaska) AAS, paper 99–451.
Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S.D.: 2000, Chaos 10, 427.
Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S.D.: 2001a, Celestial Mech. Dyn. Astron 81, 27.
Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S.D.: 2001b, Celestial Mech. Dyn. Astron 81, 63.
Koon, W.S., Lo, M.W., Marsden, J.E. and Ross, S.D.: 2002, Contemp. Math. Am. Math. Soc. 292, 129.
Llibre, J. and Simó, C.: 1980, J. Differential Equations 37, 444.
Llibre, J., Martínez, R. and Simó, C.: 1985, J. Differential Equations 58, 104.
Lo, M. and Ross, S.: 1997, JPL IOM 312/97, 2–4.
McGehee, R.P.: 1969, PhD Thesis, University of Wisconsin.
Poincaré, H.: 1957, Le méthodes nonvelles de la mécanique céleste, Dover, New York.
Simó, C. and Stuchi, T.J.: 2000, Physica D 140, 1.
Simmons, J., McDonald, A. and Brown, J.: 1985, Celestial Mechanics 35, 145.
Strömgren, E.: 1935, Publ. Copenhague Obs. No. 100.
Szebehely, V.G.: 1967, Theory of Orbits, Academic Press, London and New York.
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Papadakis, K.E. Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem. Astrophys Space Sci 302, 67–82 (2006). https://doi.org/10.1007/s10509-005-9007-6
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DOI: https://doi.org/10.1007/s10509-005-9007-6