The detection of the extrasolar planet V391 Pegasi b orbiting close to an extreme horizontal branch star could be a first sign of survival of the red-giant expansion for planets with orbital distances of less than 2 U A of their parent stars ... In about five billion years, the Sun should dramatically expand and engulf the Earth. Does actually this tragic fate of our blue planet call into question ? We studied a simplified model of a two-body problem with variable mass where mass loss is similar to a fast phenomenon like "Helium flash". First, the study is resumed in a classic way (cartesian coordinates, elliptic elements) and secondly, the problem is reformulated in the Hamiltonian formalism with the help od Delaunay elements. In a general way, mass loss modifies the orbit and implies a removal of the planet. A more detailed study of the system with a specific choice of the loss mass law allowed us to establish various models. Resuming the periodic model, it is possible to introduce an adiabatic invariant which the analytical expression is not easy to use. This adiabatic invariant allowed us to study the long-term evolution and the tidal effect on the system. The latter involve different fates for the planet considering the ratio between angular velocity of the star and mean motion of the planet.
Problème des deux corps à masse variable et soumis à l'effet de marée : étude du système V391 Pegasi
Verheylewegen, E. (Author). 2009
Student thesis: Master types › Master in Mathematics