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October  2004, 11(4): 843-854. doi: 10.3934/dcds.2004.11.843

On the accuracy of restricted three-body models for the Trojan motion

Frederic Gabern 1, , Àngel Jorba 1, and  Philippe Robutel 2,

1. 

Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona
2. 

Astronomie et Systèmes Dynamiques, IMCCE-Observatoire de Paris, 77 Av. Denfert-Rochereau, 75014 Paris, France

Received  November 2002 Revised  October 2003 Published  September 2004

In this note we compare the frequencies of the motion of the Trojan asteroids in the Restricted Three-Body Problem (RTBP), the Elliptic Restricted Three-Body Problem (ERTBP) and the Outer Solar System (OSS) model. The RTBP and ERTBP are well-known academic models for the motion of these asteroids, and the OSS is the standard model used for realistic simulations.
Our results are based on a systematic frequency analysis of the motion of these asteroids. The main conclusion is that both the RTBP and ERTBP are not very accurate models for the long-term dynamics, although the level of accuracy strongly depends on the selected asteroid.
Keywords: Symplectic integrators, frequency analysis, Trojan asteroids..
Mathematics Subject Classification: 70F1.
Citation: Frederic Gabern, Àngel Jorba, Philippe Robutel. On the accuracy of restricted three-body models for the Trojan motion. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 843-854. doi: 10.3934/dcds.2004.11.843
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