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.
Similar content being viewed by others
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
R. Bien J. Schubart (1984) ArticleTitle‘Trojan orbits in secular resonances’ Celest. Mech. Dynam. Astron. 34 425–434
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
R. Dvorak K. Tsiganis (2000) ArticleTitle‘Why do Trojan ASCs (not) escape?’ Celest. Mech. Dynam. Astron. 78 125–136 Occurrence Handle10.1023/A:1011120413687
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
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
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
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
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
A. Giorgilli C. Skokos (1997) ArticleTitle‘On the stability of the Trojan asteroids’ Astron. Astrophys. 317 254–261
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
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
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
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
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
F. Marzari H. Scholl (2002) ArticleTitle‘On the instability of Jupiter’s Trojans’ Icarus 159 328–338 Occurrence Handle10.1006/icar.2002.6904
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
A. Milani (1993) ArticleTitle‘The Trojan asteroid belt: proper elements, stability, chaos and families’ Celest. Mech. Dynam. Astron. 57 59–94
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
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
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
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
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
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
C. Skokos A. Dokoumetzidis (2000) ArticleTitle‘Effective stability of the Trojan asteroids’ Astron. Astrophys. 367 729–736 Occurrence Handle10.1051/0004-6361:20000456
K. Tsiganis H. Varvoglis R. Dvorak (2005) ArticleTitle‘Chaotic diffusion and effective stability of Jupiter Trojans’ Celest. Mech. Dynam. Astron. 92 73
C. Yoder (1979) ArticleTitle‘Notes on the origin of the Trojan asteroids’ Icarus 40 341–344 Occurrence Handle10.1016/0019-1035(79)90024-1
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10569-004-5976-y