Théorie du Mouvement du Satellite Artificiel :
Développement des Equations du Mouvement Moyen -
Application à l'Etude des Longues Périodes -

Abstract : The aim of this work is to elaborate a method permitting to obtain geodynamical information from long period variations in the motion of an artificial satellite. Short period phenomena are sometimes difficult to be modelised with precision and are at the origin of numerical difficulties while integrating the differential system of the motion over long periods of time. This is the reason why a direct study of the part of motion which does not contain the short period variations (periods shorter than 1 day) isproposed.
In the evolution of variablesdescribing the satellite's motion it is possible to artificially separate the short period variations from the long period ones (including secular variations). The latter describe an imaginary motion designated by mean centered motion. A given algorythm permits the construction of the differential system describing the mean centered motion by analytical transformation of the initial system. For most of the perturbations it was possible to use the hamiltonian formalism and the theory of canonical transformations with the Lie method . Thus were treated
perturbations due to the terrestrial potential, to a third body, to ocean and solid earth tides. This required quite important algebric manipulations which were carried out with a series processor.
The mean differential system obtained can be numerically integrated with a
very large step (about 12 hours, instead of a few minutes for the initial system). The computation time is thus divided by a factor superior to 10 (the gain differs according to the perturbations) and the numerical errors are insignificant. Precise calculations on continuous arcs of several tens of years then become more reachable. The results yielded by integration can be compared with observations previously treated in an adequate way. Simulated observations permitted the validation of the method.
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Gilles Métris. Théorie du Mouvement du Satellite Artificiel :
Développement des Equations du Mouvement Moyen -
Application à l'Etude des Longues Périodes -. Astrophysique [astro-ph]. Observatoire de Paris, 1991. Français. ⟨tel-00011585⟩

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