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ÉTUDE DES PERTURBATIONS INDUITES PAR LES ASTÉROÏDES SUR LES MOUVEMENTS DES PLANÈTES ET DES SONDES SPATIALES AUTOUR DU POINT DE LAGRANGE L2

Abstract : The purpose of this thesis is the improvement of the asteroid model in the planetary ephemeris INPOP (Intégration Numérique Planétaire de l'Observatoire de Paris). Asteroids are particularly difficult to implement in the dynamical model of an ephemeris because of their large number and because of the lack of accurate measurements of their masses. An analytical framework, suitable for the study of asteroid perturbations, is presented. After numerically searching for the most perturbing asteroids in terms of the amplitude of the individual perturbations induced on the planets, we explore a new approach. This consists in searching for a limited number of objects that should be removed from a selection of 25000 asteroids in order to achieve the best similarity between the perturbation induced by the remaining asteroids and the perturbation induced by a solid ring centered on the Sun. The problem falls into the category of mixed integer quadratic problems where real as well as integer parameters are fitted in order to obtain an optimal solution. We provide a new list of 276 asteroids that together with a ring should be accounted for in the dynamical model of the ephemeris. As the optimal selection depends on asteroid masses, the list is based on Monte Carlo experiments in which the asteroid masses are randomly varied within reasonable intervals. The Tikhonov regularization with box constraints is presented as a method to fit the new model to observations. A second part of the study is concerned with asteroid perturbations induced on spacecrafts orbiting the Earth-Sun Lagrangian point L2. The point harbors since 2009 the Herschel and Planck observatories, it was also selected for the incoming Gaia mission. The nominal orbits of Herschel and Planck are determined by calculating the normal form for the circular restricted 3 body problem hamiltonian. The orbits are then injected into INPOP and stabilized by the multiple-shooting method. An analytical framework based on the quasi-bicircular problem is developed to predict the perturbations induced on the spacecrafts by asteroids on circular orbits. The perturbations induced by asteroids on realistic orbits are obtained numerically by comparing integrations with INPOP of both spacecrafts in presence of various asteroids. We show that in general the perturbations induced by the asteroids are negligible.
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Contributor : Petr Kuchynka <>
Submitted on : Wednesday, January 19, 2011 - 12:01:17 PM
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  • HAL Id : tel-00557567, version 1

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Petr Kuchynka. ÉTUDE DES PERTURBATIONS INDUITES PAR LES ASTÉROÏDES SUR LES MOUVEMENTS DES PLANÈTES ET DES SONDES SPATIALES AUTOUR DU POINT DE LAGRANGE L2. Planète et Univers [physics]. Observatoire de Paris, 2010. Français. ⟨tel-00557567⟩

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