4 juin - 7 juin 2013

Abstract

S06 Astrom├ętrie de haute pr├ęcision et applications

Stochastic perturbation of the two-body problem

F.PIERRET, J.CRESSON, B.PUIG, C.LE PONCIN-LAFITTE

In this study we present the impact of a stochastic perturbation on the classical two-body problem. First, we discuss the existence of first integrals by introducing a new kind of conservation laws. Second we show how to define a Hamiltonian structure under stochastic perturbation. Finally, we illustrate numerically the stochastic variation of osculating elements as the semi-major axis, the eccentricity and the pericenter. We conclude with an analysis on how to construct a new set of Gauss's equations in the planar case.