Abstract
Numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses (Δϖ = 0) or anti-aligned periapses (Δϖ = π), librations around stationary asymmetric solutions in which the periapses configuration is fixed, but with Δϖ taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axes drift, the solutions show turnabouts from one configuration to another. The presented results are valid for other non-conservative anti-dissipative forces leading to adiabatic convergent migration and capture into one of these resonances.
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References
Aksnes, K. and Franklin, F. A.: 2001, 'Secular acceleration of Io derived from mutual satellite events', Astron. J. 122, 2734-2739.
Beaugé, C.: 1994, 'Asymmetric librations in exterior resonances', Celest. Mech. & Dyn. Astr. 60, 225-248.
Beaugé, C., Ferraz-Mello, S. and Michtchenko, T. A.: 2003, 'Extrasolar planets in mean-motion resonance: apsidal and asymmetric stationary solutions', Astrophys. J. (in press).
Callegari Jr., N., Michtchenko, T. A. and Ferraz-Mello, S.: 2003, 'Dynamics of two planets in the 2:1 mean-motion resonances' (in preparation).
Everhart, E.: 1985, 'An efficient integrator that uses Gauss-Radau spacings'. In: A. Carusi and G. B. Valsecchi (eds), Dynamics of Comets: Their Origin and Evolution, Reidel, Dordrecht, 185.
Ferraz-Mello, S.: 1979, Dynamics of the Galilean Satellites, IAG-USP, São Paulo.
Ferraz-Mello, S.: 1987, 'Averaging the elliptic asteroidal problem near a first-order resonance', Astron. J. 94, 208-212.
Gomes, R. S.: 1998, 'Orbital evolution in resonance lock. II. Two mutually perturbing bodies', Astron. J. 116, 997-1005.
Hadjidemetriou, J. D.: 2002, 'Resonant periodic motion and the stability of the extrasolar planetary systems', Celest. Mech. & Dyn. Astr. 83, 141-154.
Hadjidemetriou, J. D. and Psychoyos, D.: 2003, 'Dynamics of extrasolar planetary systems: 2/1 resonant motion', Lect. Notes in Phys. (in press).
Jancart, S.: 2002, Résonances et Dissipations, PhD. Thesis, Presses Universitaires, Namur.
Jancart, S., Lemaitre, A. and Istace, A.: 2002, 'Second fundamental model of resonance with asymmetric equilibria', Celest. Mech. & Dyn. Astr. 84, 197-221.
Ji, J. H., Kinoshita, H., Liu, L., Li, G. Y. and Nakai, H.: 2003, 'The apsidal antialignment of the HD 82943 system', Celest. Mech. & Dyn. Astr. 87, 113-120 (this issue).
Kley, W.: 2003, 'Dynamical evolution of planets in disks. Planets in resonant orbits', Celest. Mech. & Dyn. Astr. 87, this issue.
Lee, M. H. and Peale, S. J.: 2002, 'Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets', Astrophys. J. 567, 596-609.
Lee, M. H. and Peale, S. J.: 2003, 'Extrasolar planets and mean-motion resonances', ASP Conf. Ser. (in press).
Lieske, J. H.: 1987, 'Galilean satellites evolution-observational evidence for secular changes in mean-motions', Astron. Astrophys. 176, 146-158.
Lieske, J. H.: 1998, 'Galilean satellites ephemerides E5', Astron. Astrophys. Suppl. Ser. 129, 205-217.
Mignard, F.: 1981, 'The evolution of the Lunar orbit revisited. I', Moon and Planets, 20, 301-315.
Murray, N., Paskowitz, M. and Holman, M.: 2002, 'Eccentricity evolution of resonant migrating planets', Astrophys. J. 565, 608-620.
Peale, S. J.: 1999, 'Origin and evolution of the natural satellites', Ann. Rev. Astron. Astrophys. 37, 533-602.
Peale, S. J.: 2003, 'Tidally driven volcanism', Celest. Mech. & Dyn. Astr. 87, this issue.
Tisserand, F.: 1896, Traité de Mécanique Céleste, Vol. IV, Gauthier-Villars, Paris.
Touma, J. and Wisdom, J.: 1994, 'Evolution of the Earth-Moon system', Astron. J. 108, 1943-1961.
Wu, Y. and Goldreich, P.: 2002, 'Tidal evolution of the planetary system around HD 83443', Astrophys. J. 564, 1024-1027.
Yoder, C. F.: 1979, 'How tidal heating in Io drives the Galilean orbital resonance locks', Nature 279, 767-770.
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Ferraz-Mello, S., Beaugé, C. & Michtchenko, T.A. Evolution of Migrating Planet Pairs in Resonance. Celestial Mechanics and Dynamical Astronomy 87, 99–112 (2003). https://doi.org/10.1023/A:1026126716612
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DOI: https://doi.org/10.1023/A:1026126716612