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Numerical studies of chaotic hilda-type orbits. (English) Zbl 1165.70018

Summary: Earlier work indicates a comparatively rapid chaotic evolution of the orbits of some Hilda asteroids that move at the border of the domain occupied by the characteristic parameters of the objects at the 3/2 mean motion resonance. A simple Jupiter-Saturn model of the forces leads to numerical results on some of these cases and allows a search for additional resonances that can contribute to the chaotic evolution. In this context the importance of the secondary resonances that depend on the period of revolution of the argument of perihelion is pointed out. Among the studied additional resonances, there are three-body resonances with arguments that depend on the mean longitudes of Jupiter, Saturn, and asteroid, but on slowly circulating angular elements of the asteroid as well, and the frequency of these arguments is close to a rational ratio with respect to the frequency of the libration due to the basic resonance.

MSC:

70F15 Celestial mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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[1] Knežević Z., Milani A.: Synthetic proper elements for outer main belt asteroids. Celest. Mech. Dyn. Astron. 78, 17–46 (2000) · Zbl 0992.85502
[2] Morbidelli A., Moons M.: Secular resonances in mean motion commensurabilities: the 2/1 and 3/2 cases. Icarus 102, 316–332 (1993)
[3] Nesvorný D., Ferraz-Mello S.: On the asteroidal population of the first-order jovian resonances. Icarus 130, 247–258 (1997)
[4] Schubart J.: Three characteristic parameters of orbits of Hilda-type asteroids. Astron. Astrophys. 114, 200–204 (1982)
[5] Schubart, J.: The low-eccentricity gap at the Hilda group of asteroids. In: Lagerkvist, C.-I., Rickman, H., et al. (eds.) Asteroids, Comets, Meteors III, pp. 171–174. Reprocentralen HSC, Uppsala (1990)
[6] Schubart J.: Additional results on orbits of Hilda-type asteroids. Astron. Astrophys. 241, 297–302 (1991)
[7] Schubart J.: Additional effects of resonance in Hilda-asteroid orbits by the combined action of Jupiter and Saturn. Icarus 188, 189–194 (2007)
[8] Schubart J., Stumpff P.: On an N-body program of high accuracy for the computation of ephemerides of minor planets and comets. Veröffentl. Astron. Rechen-Inst. Heidelberg 18, 1–31 (1966)
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