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

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A Comparison of the Dynamical Evolution of Planetary Systems
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Abstract

In this paper, we make a systematic study of the global dynamical structure of the Sun-Jupiter L 4 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

  • Beaugé, C. and Roig, F.: 2001, ‘A semianalytical model for the motion of the trojan asteroids: proper elements and families’, Icarus 153, 391–415.

    Article  ADS  Google Scholar 

  • Bien, R. and Schubart, J.: 1984, ‘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.

    Google Scholar 

  • Celletti, A. and Giorgilli, A.: 1991, ‘On the stability of the Lagrangian points in the spatial restricted three body problem’, Celest. Mech. Dynam. Astron. 50(1), 31–58.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Dvorak, R. and Tsiganis, K.: 2000, ‘Why do Trojan ASCs (not) escape?’, Celest. Mech. Dynam. Astron. 78, 125–136.

    Article  ADS  MATH  Google Scholar 

  • Ferraz-Mello, S.: 1997, ‘A symplectic mapping approach to the study of the stochasticity in asteroidal resonances’, Celest. Mech. Dynam. Astron. 65, 421–437.

    Article  ADS  MATH  Google Scholar 

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

    Google Scholar 

  • Gabern, F. and Jorba, A.: 2001, ‘A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system’. Discrete Contin. Dyn. Syst. Series B 1(2), 143–182.

    Article  MathSciNet  MATH  Google Scholar 

  • Gabern, F. and Jorba, A.: 2004, ‘Generalizing the restricted three-body problem. the bianular and tricircular coherent problems’, Astron. Astrophys. 420, 751–762.

    Article  ADS  MATH  Google Scholar 

  • Gabern, F., Jorba, A. and Robutel, P.: 2004, ‘On the accuracy of restricted three-body models for the trojan motion’, Discrete Contin. Dyn. Syst. 11(4), 843–854.

    Article  MathSciNet  MATH  Google Scholar 

  • Giorgilli, A., Delshams, A., Fontich, E., Galgani, L. and Simó, C.: 1989, ‘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.

    Article  MathSciNet  MATH  Google Scholar 

  • Giorgilli, A. and Skokos, C.: 1997, ‘On the stability of the Trojan asteroids’. Astron. Astrophys. 317, 254–261.

    ADS  Google Scholar 

  • Jorba, À. and Villanueva, J.: 1997, ‘On the persistence of lower dimensional invariant tori under quasi-periodic perturbations’, J. Nonlinear Sci. 7, 427–473.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Laskar, J.: 1990, ‘The chaotic motion of the solar system. A numerical estimate of the size of the chaotic zone’, Icarus 88, 266–291.

    Article  ADS  Google Scholar 

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

    Google Scholar 

  • Laskar, J. and Robutel, P.: 2001, ‘High order symplectic integrators for perturbed Hamiltonian systems’, Celest. Mech. Dynam. Astron. 80, 39–62.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Levison, H., Shoemaker, E. and Shoemaker, C.: 1997, ‘The long-term dynamical stability of Jupiter’s Trojan asteroids’, Nature 385, 42–44.

    Article  ADS  Google Scholar 

  • Marzari, F. and Scholl, H.: 2002, ‘On the instability of Jupiter’s Trojans’. Icarus 159, 328–338.

    Article  ADS  Google Scholar 

  • Michtchenko, T., Beaugé, C. and Roig, F.: 2001, ‘Planetary migration and the effects of mean motion resonances on Jupiter’s Trojan asteroids’, Astron. J. 122, 3485–3491.

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  • Milani, A. and Nobili, A. M.: 1992, ‘An example of stable chaos in the Solar System’, Nature 357, 569–571.

    Article  ADS  Google Scholar 

  • Milani, A., Nobili, A. M. and Knezevic, Z.: 1997, “Stable chaos in the asteroid bel’, Icarus 125, 13–31.

    Article  ADS  Google Scholar 

  • Nesvorny, D. and Dones, L.: 2002, “How long-live are the hypothetical Trojan populations of Saturn, Uranus, and Neptune?’, Icarus 160, 271–288.

    Article  ADS  Google Scholar 

  • Nesvorny, D., Thomas, F. Ferraz-Mello, S. and Morbidelli, A.: 2002, “A perturbative treatment of the co-orbital motion’, Celest. Mech. Dynam. Astron. 82, 323–361.

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Robutel, P. and Laskar, J.: 2001, ‘Frequency map and global dynamics in the solar system I’, Icarus 152, 4–28.

    Article  ADS  Google Scholar 

  • Skokos, C. and Dokoumetzidis, A.: 2000, ‘Effective stability of the Trojan asteroids’, Astron. Astrophys. 367, 729–736.

    Article  ADS  Google Scholar 

  • Tsiganis, K., Varvoglis, H. and Dvorak, R.: 2005, ‘Chaotic diffusion and effective stability of Jupiter Trojans’, Celest. Mech. Dynam. Astron. 92, 73, 89.

    Article  MathSciNet  Google Scholar 

  • Yoder, C.: 1979, ‘Notes on the origin of the Trojan asteroids’, Icarus 40, 341–344.

    Article  ADS  Google Scholar 

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Rudolf Dvorak Sylvio Ferraz-Mello

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Robutel, P., Gabern, F., Jorba, A. (2005). The Observed Trojans and the Global Dynamics Around the Lagrangian Points of the Sun-Jupiter System. In: Dvorak, R., Ferraz-Mello, S. (eds) A Comparison of the Dynamical Evolution of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4466-6_4

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  • DOI: https://doi.org/10.1007/1-4020-4466-6_4

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4218-8

  • Online ISBN: 978-1-4020-4466-3

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