Abstract
In this work we consider four families of plane periodic orbits direct around the Sun which approach Jupiter but they are sufficiently far from it so as to be considered as predominantly two body orbits of the Sun-asteroid system. We study their horizontal and vertical stabilities and we give the exact orbits of bifurcations of these families with three-dimensional families of the same multiplicity or twice the multiplicity of the above families of plane symmetric periodic orbits. Moreover, we give the first segments of the three dimensional families of symmetric periodic orbits which emanate from these plane bifurcations and we study their stability relating it with the stability of the plane bifurcations.
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References
Kazantzis, P.: 1978, Astrophys. Space Sci. 59, 355.
Szebehely, V.: 1963, Space Sci. Rev. 2, 219.
Szebehely, V.: 1979, ‘Zentralblatt fur Mathematik und ihre Grenzgebiete’, Mathematics Abstracts, Band, 393 (70011).
Kazantzis, P.: 1979a, Astrophys. Space Sci. 61, 357.
Kazantzis, P.: 1979b, Astrophys. Space Sci. 61, 477.
Kazantzis, P.: 1979c, Astrophys. Space Sci. 65, 493.
Kazantzis, P.: 1980, Astrophys. Space Sci. 69, 353.
Zagouras, C. and Kazantzis, P.: 1979, Astrophys. Space Sci. 61, 389.
Zagouras, C.: 1985, Celest. Mech. 37, 27.
Perdios, E., et al.: 1991, Celest. Mech. Dyn. Astron. 51, 349.
Papadakis, K. and Zagouras, C.: 1993, Astrophys. Space Sci. 199, 241.
Zagouras, C. and Moran, P.: 1981, The Moon and the Planets 25, 67.
Markellos, V. and Kazantzis, P.: 1975, Celest. Mech. 15, 35.
Markellos, V.: 1976, Astrophys. Space Sci. 43, 449.
Markellos, V. and Zagouras, C.: 1977, Astron. Astrophys. 59, 79.
Henon, M.: 1965a, Ann. Astrophys. 28, 499.
Henon, M.: 1965b, Ann. Astrophys. 28, 992.
Henon, M.: 1973a, Astron. Astrophys. 28, 415.
Henon, M.: 1973b, Ann. Astrophys. 30, 317.
Zagouras, C. and Markellos, V.: 1977, Astron. Astrophys. 59, 79.
Goudas, C.: 1961, Bull. Soc. Math. Grece, Nouvelle Serie 2, 1.
Bray, T. and Goudas, C.: 1967, in: Z. Kopal (ed.), Adv. Astron. Astrophys. 5, 72.
Hadjidemetriou, J.: 1975, Celest. Mech. 12, 267.
Henon, M.: 1976, Celest. Mech. 13, 277.
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Kazantzis, P. The Structure of Periodic Solutions in the Restricted Problem of the Three Bodies II. Astrophysics and Space Science 249, 7–29 (1997). https://doi.org/10.1023/A:1000254913612
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DOI: https://doi.org/10.1023/A:1000254913612