SEMINAIRE MERCREDI 14 AVRIL 2004
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Àngel Jorba
Departament de Matemàtica Aplicada i Anàlisi 
Universitat de Barcelona 
Gran Via 585 
08007 Barcelona 
Spain 

Title: Dynamics near the Lagrangian points of the real Earth-Moon system

Abstract: In this work we consider the motion of an infinitesimal particle near
the equilateral points of the real Earth-Moon system. We use, as real
system, the one provided by the JPL ephemeris: the ephemeris give the
positions of the main bodies of the solar system (Earth, Moon, Sun and
planets) so it is not difficult to write the vector field for the
motion of a small particle under the attraction of those bodies.
Numerical integrations of this vector field show that trajectories
with initial conditions in a vicinity of the equilateral points escape
after a short time. On the other hand, it is known that the Restricted
Three Body Problem is not a good model for this problem, since it
predicts a quite large region of practical stability. For this reason,
we will discuss some intermediate models that try to account for the
effect of the Sun and the eccentricity of the Moon. As we will see,
they are more similar to the real system in the sense that the
vicinity of the equilateral points is also unstable. However, these
models have some families of lower dimensional tori (2-D and 3-D),
some of them elliptic and some of them hyperbolic. The elliptic ones
give rise to a region of effective stability at some distance of the
triangular points in the above mentioned models. It is remarkable that
these regions seem to persist in the real system, at least for time
spans of 1000 years.