Abstract
In this paper, we study circular orbits of the J 2 problem that are confined to constant-z planes. They correspond to fixed points of the dynamics in a meridian plane. It turns out that, in the case of a prolate body, such orbits can exist that are not equatorial and branch from the equatorial one through a saddle-center bifurcation. A closed-form parametrization of these branching solutions is given and the bifurcation is studied in detail. We show both theoretically and numerically that, close to the bifurcation point, quasi-periodic orbits are created, along with two families of reversible orbits that are homoclinic to each one of them.
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References
Arnold, V. I., Kozlov, V. V. and Neishtadt, A. I.: 1997, Mathematical Aspects of Classical and Celestial Mechanics, Springer Verlag, Berlin.
Broucke, R. A.: 1994, 'Numerical integration of periodic orbits in the main problem of artificial satellite theory', Celest. Mech. & Dyn. Astr. 58, 99uu123.
Champneys, A.: 1998, 'Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics', Physica D 112, 158uu186.
Coffey, S., Deprit, A. and Deprit, E.: 1994, 'Frozen orbits for satellites close to an earth-like planet', Celest. Mech. & Dyn. Astr. 59, 37uu72.
Celetti, A., Della Penna, G. and Falconi, C.: 2000, 'Analytical construction of families of periodic orbits for the J2, problem' University of Roma 'Tor Vegata', Preprint.
Iooss, G. and Adelmayer, M.: 1998, Topics in Bifurcation Theory and Applications, Advanced Series in Nonlinear Dynamics 3, World Scientific.
Langbort, C.: 2000, 'Le flambage d'une poutre comme un système spatial reversible', M.S. Dissertation, Université de Nice.
Lara, M.: 1997, 'On periodic polar orbits in the artificial satellite problem', J. Astr. Sci. 45, 321uu328.
Lombardi, E.: 2000, Oscillatory Integrals and Phenomena Beyond All Algebraic Order, with Applications to Homoclinic Orbits in Reversible Systems, Lecture Notes in Mathematics, Springer Verlag, Berlin.
Lombardi, E.: 1999, 'Non persistence of homoclinic connections for perturbed integrable reversible systems', J. Dyn. Diff. Eqns. 11, 124uu208.
Lombardi, E.: 1996, 'Homoclinic orbits to small periodic orbits for a class of reversible systems', Proc. Roy. Soc. Edin. A 126, 1035uu1054.
Scheeres, D. J.: 1994, 'Dynamics about uniformly rotating triaxial ellipsoids, applications to asteroids', Icarus 110, 225uu238.
Scheeres, D. J., Ostro, S. J., Hudson, R. S., De Jong, E. H. and Suzuki, S.: 1998, 'Dynamics of orbits close to asteroid 4179 Toutatis', Icarus 132, 53uu79.
Scheeres, D. J., Ostro, S. J., Hudson, R. S. and Werner, R. A.: 1996, 'Orbits close to asteroid 4769 Castalia', Icarus 121, 67uu87.
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Langbort, C. Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body. Celestial Mechanics and Dynamical Astronomy 84, 369–385 (2002). https://doi.org/10.1023/A:1021185011071
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DOI: https://doi.org/10.1023/A:1021185011071