An Upper Limit of Mass for a Stable Minor Planet in the Main Asteroid Belt |
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| Institution: | 1. Department of Geophysical, Atmospheric and Planetary Sciences, Tel-Aviv University, Israel;2. Institute for Astrophysics of Andalusia (IAA-CSIC), Granada, Spain;3. Department of Life and Natural Sciences, The Open University of Israel, Ra’anana, Israel;4. Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands;1. Université de Franche-Comté, Institut UTINAM, CNRS/INSU, UMR 6213, Observatoire des Sciences de l?Univers de Besançon, France;2. Atmospheric, Oceanic & Planetary Physics, Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK;3. LPC2E, CNRS-Université d?Orléans, 3a Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France;4. LESIA, Observatoire de Paris, CNRS, UPMC, Univ. Paris-Diderot, 5, place Jules Janssen, F-92195 Meudon Cedex, France;5. Space Science & Planetology, Physics Institute, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland;6. Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany;7. Department of Geophysics, Atmospheric and Planetary Sciences, Tel-Aviv University, Tel-Aviv, Israel;8. Planetary and Space Sciences, Department of Physics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK;9. Institute for Physics, University of Rostock, 18051 Rostock, Germany;10. CRPG-CNRS, Nancy-Université, 15 rue Notre Dame des Pauvres, 54501 Vandoeuvre-ls-Nancy, France;11. Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium;12. Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844-1023, USA;13. Southwest Research Institute (SwRI), 6220 Culebra Road, San Antonio, TX 78228, USA;14. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA;15. NASA Goddard Space Flight Center, Code 690, Greenbelt, MD 20771, USA;p. Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109-2143, USA;q. Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS/Université Toulouse III (UMR 5277), 9, avenue du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France;r. University of Athens, Department of Physics, Panepistimioupoli Zografou, 15784 Athens, Greece;s. Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042 Graz, Austria;t. Stockholm University Astrobiology Centre, Department of Physics, AlbaNova, Stockholm University/Stockholms universitet, Roslagstullbacken 21, S-10691 Stockholm, Sweden/Sverige;u. Observatoire de la Côte d?Azur, Laboratoire Lagrange, BP 4229, 06304 Nice cedex 4, France;v. Department of Physics, University of Idaho, Moscow ID 83843;w. Departamento Física Aplicada I, Universidad del País Vasco UPV/EHU, ETS Ingeniería, Alameda Urquijo s/n, 48013 Bilbao, Spain;x. Unidad Asociada Grupo Ciencias Planetarias UPV/EHU-IAA(CSIC), 48013 Bilbao, Spain;y. Center for Radiophysics and Space Research, Space Sciences Building, Cornell University, Ithaca, NY 14853, USA;z. School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK;11. Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK;12. Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, Institut Pierre Simon Laplace, Paris, France;13. Solar System Science & Exploration, Monrovia, USA;14. Thales Alenia Space, Cannes, France;1. CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, China;2. School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China;1. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China;2. School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China;3. Shanghai Key Laboratory of Space Navigation and Position Techniques, Shanghai 200030, China;4. Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing 210093, China;1. INRIM, Strada delle Cacce 91, I-10135 Torino, Italy;2. Politecnico di Torino, Dipartimento di Scienza Applicata e Tecnologia, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy |
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| Abstract: | The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)3 is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 108 years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 1025 kg, i.e., about the Earth's mass. |
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