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The Observed Trojans and the Global Dynamics Around The Lagrangian Points of the Sun–Jupiter System

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Abstract

In this paper, we make a systematic study of the global dynamical structure of the Sun–Jupiter L4 tadpole region. The results are based on long-time simulations of the Trojans in the Sun, Jupiter, Saturn system and on the frequency analysis of these orbits. We give some initial results in the description of the resonant structure that guides the long-term dynamics of this region. Moreover, we are able to connect this global view of the phase space with the observed Trojans and identify resonances in which some of the real bodies are located.

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References

  • C. Beaugé F. Roig (2001) ArticleTitle‘A semianalytical model for the motion of the trojan asteroids: proper elements and families’ Icarus 153 391–415 Occurrence Handle10.1006/icar.2001.6699

    Article  Google Scholar 

  • R. Bien J. Schubart (1984) ArticleTitle‘Trojan orbits in secular resonances’ Celest. Mech. Dynam. Astron. 34 425–434

    Google Scholar 

  • Bowell, E.: 2001, ‘The asteroid orbital elements database’. For more information, visit the URL http://www.naic.edu/˜nolan/astorb.html.

  • A. Celletti A. Giorgilli (1991) ArticleTitle‘On the stability of the Lagrangian points in the spatial restricted three body problem’ Celest. Mech. Dynam. Astron. 50 IssueID1 31–58 Occurrence Handle10.1007/BF00048985

    Article  Google Scholar 

  • R. Dvorak K. Tsiganis (2000) ArticleTitle‘Why do Trojan ASCs (not) escape?’ Celest. Mech. Dynam. Astron. 78 125–136 Occurrence Handle10.1023/A:1011120413687

    Article  Google Scholar 

  • S. Ferraz-Mello (1997) ArticleTitle‘A symplectic mapping approach to the study of the stochasticity in asteroidal resonances’ Celest. Mech. Dynam. Astron. 65 421–437 Occurrence Handle10.1007/BF00049505

    Article  Google Scholar 

  • Gabern, F.: 2003, ‘On the dynamics of the Trojan asteroids’. Ph.D. thesis, University of Barcelona. http://www.maia.ub.es/∼gabern/.

  • F. Gabern A. Jorba (2001) ArticleTitle‘A restricted four-body model for the dynamics near the Lagrangian points of the Sun–Jupiter system’ Discrete Contin. Dyn. Syst. Series B 1 IssueID2 143–182

    Google Scholar 

  • F. Gabern A. Jorba (2004) ArticleTitle‘Generalizing the restricted three-body problem. the bianular and tricircular coherent problems’ Astron. Astrophys. 420 751–762 Occurrence Handle10.1051/0004-6361:20035799

    Article  Google Scholar 

  • F. Gabern A. Jorba P. Robutel (2004) ArticleTitle‘On the accuracy of restricted three-body models for the trojan motion’ Discrete Contin. Dyn. Syst. 11 IssueID4 843–854

    Google Scholar 

  • A. Giorgilli A. Delshams E. Fontich L. Galgani C. Simó (1989) ArticleTitle‘Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem’ J. Differential Equations 77 167–198 Occurrence Handle10.1016/0022-0396(89)90161-7

    Article  Google Scholar 

  • A. Giorgilli C. Skokos (1997) ArticleTitle‘On the stability of the Trojan asteroids’ Astron. Astrophys. 317 254–261

    Google Scholar 

  • À. Jorba J. Villanueva (1997) ArticleTitle‘On the persistence of lower dimensional invariant tori under quasi-periodic perturbations’ J. Nonlinear Sci. 7 427–473 Occurrence Handle10.1007/s003329900036

    Article  Google Scholar 

  • J. Laskar (1990) ArticleTitle‘The chaotic motion of the solar system A numerical estimate of the size of the chaotic zone’ Icarus 88 266–291 Occurrence Handle10.1016/0019-1035(90)90084-M

    Article  Google Scholar 

  • J. Laskar (1999) ‘Introduction to frequency map analysis’ C. Simó (Eds) Hamiltonian Systems with Three or More Degrees of Freedom NATO ASI. Kluwer Academic Publishers Dordrecht 134–150

    Google Scholar 

  • J. Laskar P. Robutel (2001) ArticleTitle‘High order symplectic integrators for perturbed Hamiltonian systems’ Celest. Mech. Dynam. Astron. 80 39–62 Occurrence Handle10.1023/A:1012098603882

    Article  Google Scholar 

  • H. Levison E. Shoemaker C. Shoemaker (1997) ArticleTitle‘The long-term dynamical stability of Jupiter’s Trojan asteroids’ Nature 385 42–44 Occurrence Handle10.1038/385042a0

    Article  Google Scholar 

  • F. Marzari H. Scholl (2002) ArticleTitle‘On the instability of Jupiter’s Trojans’ Icarus 159 328–338 Occurrence Handle10.1006/icar.2002.6904

    Article  Google Scholar 

  • T. Michtchenko C. Beaugé F. Roig (2001) ArticleTitle‘Planetary migration and the effects of mean motion resonances on Jupiter’s Trojan asteroids’ Astron. J. 122 3485–3491 Occurrence Handle10.1086/324464

    Article  Google Scholar 

  • A. Milani (1993) ArticleTitle‘The Trojan asteroid belt: proper elements, stability, chaos and families’ Celest. Mech. Dynam. Astron. 57 59–94

    Google Scholar 

  • Milani, A.: 1994, ‘The dynamics of the Trojan asteroids’. In: IAU Symp. 160, Asteroids, Comets, Meteors 1993, Vol. 160, pp. 159–174.

  • A. Milani A. M. Nobili (1992) ArticleTitle‘An example of stable chaos in the Solar System’ Nature 357 569–571

    Google Scholar 

  • A. Milani A. M. Nobili Z. Knezevic (1997) ArticleTitle‘Stable chaos in the asteroid belt’ Icarus 125 13–31 Occurrence Handle10.1006/icar.1996.5582

    Article  Google Scholar 

  • D. Nesvorny L. Dones (2002) ArticleTitle‘How long-live are the hypothetical Trojan populations of Saturn, Uranus, and Neptune?’ Icarus 160 271–288 Occurrence Handle10.1006/icar.2002.6961

    Article  Google Scholar 

  • D. Nesvorny F. Thomas S. Ferraz-Mello A. Morbidelli (2002) ArticleTitle‘A perturbative treatment of the co-orbital motion’ Celest. Mech. Dynam. Astron. 82 323–361 Occurrence Handle10.1023/A:1015219113959

    Article  Google Scholar 

  • P. Robutel J. Laskar (2000) ‘Global dynamics in the solar system’ H. Pretka-Ziomek E. Wnuk P. K. Seidelmann D. Richardson (Eds) Dynamics of Natural and Artificial Celestial Bodies Kluwer Academic Publishers Dordrecht 253–258

    Google Scholar 

  • P. Robutel J. Laskar (2001) ArticleTitle‘Frequency map and global dynamics in the solar system I’ Icarus 152 4–28 Occurrence Handle10.1006/icar.2000.6576

    Article  Google Scholar 

  • C. Skokos A. Dokoumetzidis (2000) ArticleTitle‘Effective stability of the Trojan asteroids’ Astron. Astrophys. 367 729–736 Occurrence Handle10.1051/0004-6361:20000456

    Article  Google Scholar 

  • K. Tsiganis H. Varvoglis R. Dvorak (2005) ArticleTitle‘Chaotic diffusion and effective stability of Jupiter Trojans’ Celest. Mech. Dynam. Astron. 92 73

    Google Scholar 

  • C. Yoder (1979) ArticleTitle‘Notes on the origin of the Trojan asteroids’ Icarus 40 341–344 Occurrence Handle10.1016/0019-1035(79)90024-1

    Article  Google Scholar 

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Robutel, P., Gabern, F. & Jorba, A. The Observed Trojans and the Global Dynamics Around The Lagrangian Points of the Sun–Jupiter System. Celestial Mech Dyn Astr 92, 53–69 (2005). https://doi.org/10.1007/s10569-004-5976-y

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