Structure of the 2:1 and 3:2 jovian resonances |
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| Institution: | 1. Institute of Physics, University of Antioquia, Medellin, Colombia;2. Department of Matemathics and Physics “E. De Giorgi”, University of Salento, Lecce, Italy;3. INAF - Istituto Nazionale di Astrofisica, Sezione Universitaria di Lecce, Lecce, Italy;4. INFN - Istituto Nazionale di Fisica Nucleare, Sezione di Lecce, Lecce, Italy;1. Astronomical Institute, Academy of Sciences of the Czech Republic, Fričova 1, CZ-25165 Ondřejov, Czech Republic;2. Modra Observatory, Department of Astronomy, Physics of the Earth, and Meteorology, FMPI UK, Bratislava SK-84248, Slovakia;3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA;4. Sugarloaf Mountain Observatory, South Deerfield, MA 01373, USA;5. Institute of Astronomy of Kharkiv National University, Sumska Str. 35, Kharkiv 61022, Ukraine;6. Sonoita Research Observatory, 77 Paint Trail, Sonoita, AZ 85637, USA;7. Department of Space Studies, Southwest Research Institute, Boulder, CO 80302, USA;8. Crimean Astrophysical Observatory, Department of Radioastronomy and Geodynamics, Simeiz 98680, Crimea;9. Physics and Astronomy Department, Appalachian State University, Boone, NC 28608, USA;10. Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovakia;11. Center for Solar System Studies, 9302 Pittsburgh Avenue, Suite 200, Rancho Cucamonga, CA 91730, USA;12. Shed of Science Observatory, 5213 Washburn Ave. S, Minneapolis, MN 55410, USA;13. Planetary Science Institute, Tucson, AZ 85719, USA;14. Badlands Observatory, 12 Ash Street, P.O. Box 37, Quinn, SD 57775, USA;15. Institute of Astronomy, Faculty of Mathematics and Physics, Charles University, Prague, V Holešovičkách 2, CZ-18000 Prague 8, Czech Republic;p. German Aerospace Center (DLR), Institute of Planetary Research, Rutherfordstr. 2, 12489 Berlin, Germany;q. Blue Mountains Observatory, Leura, NSW, Australia;r. Belgrade Astronomical Observatory, Volgina 7, 11060 Belgrade 38, Serbia;s. Astronomical Observatory Institute, Faculty of Physics, Adam Mickiewicz University, Sloneczna 36, 60-286 Poznań, Poland;t. Hunters Hill Observatory, Ngunnawal, Canberra, Australia;u. The University of Texas at Austin, Astronomy Department/McDonald Observatory, 1 University Station C1400, Austin, TX 78712-0259, USA;v. Carl Sagan Center at the SETI Institute, 189 Bernado Av., Mountain View, CA 94043, USA;w. Department of Astronomy, University of California at Berkeley, Berkeley, CA 94720, USA;x. Kharadze Abastumani Astrophysical Observatory, Ilia State University, G. Tsereteli str. 3, Tbilisi 0162, Georgia;y. Crimean Astrophysical Observatory, 98409 Nauchny, Crimea;z. Campo Catino Observatory, I-03016 Guarcino, Italy;11. The Virtual Telescope Project, I-03023 Ceccano, Italy;12. IMCCE-CNRS-Observatoire de Paris, 77 avenue Denfert Rochereau, 75014 Paris, France;13. OPERA Observatory, 33820 Saint Palais, France;14. Elginfield Observatory, Department of Physics & Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada;15. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya sq. 4, Moscow 125047, Russia;16. Physics and Astronomy Department, University of North Carolina, Chapel Hill, NC 27514, USA;1. Institute for Astronomy, University of Hawaii at Manoa, 2680 Woodlawn Drive, Honolulu, HI 96822, USA;2. Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina F1, 84248 Bratislava, Slovakia;3. Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, UK;5. Finnish Geospatial Research Institute, P.O. Box 15, 02430 Masala, Finland;6. UNS-CNRS-Observatoire de la Côte d‘Azur, BP 4229, 06304 Nice Cedex 4, France;7. GMTO Corp., 251 S. Lake Ave., Suite 300, Pasadena, CA 91101, USA |
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| Abstract: | The chaotic regions of the phase space in the vicinity of the 2:1 and 3:2 jovian resonances are identified by using a mapping technique derived from a second-order expansion of the disturbing function for the planar elliptical restricted three-body problem. It is shown that both resonances have extensive chaotic regions which in some cases can lead to large changes in the eccentricity of asteroid orbits. Although the 3:2 resonance is shown to be more chaotic than the 2:1 resonance, the existence of the Hilda group of asteroids and the Hecuba gap may be explained by distinct differences in the location of the high-eccentricity regions at each resonance. The problem of the convergence of the expansion of the disturbing function in the outer asteroid belt is also discussed. |
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