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

Frederic Gabern; Àngel Jorba; Philippe Robutel

doi:10.3934/dcds.2004.11.843

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2004, Volume 11, Issue 4: 843-854. Doi: 10.3934/dcds.2004.11.843

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

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

Received: October 31, 2002

Revised: September 30, 2003

Published: September 2004

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Abstract

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.

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Mathematics Subject Classification: 70F15.

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