TITLE:
On the dynamics near the Lagrangian points of the real
Earth-Moon system

AUTHORS:
Angel Jorba, Enric Castella
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain
E-mail: angel@maia.ub.es

ABSTRACT:
In this work we consider the motion of an infinitessimal 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 vectorfield for the
motion of a small particle under the attraction of those bodies.
Numerical integrations of this vectorfield 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 a
intermediate model that tries to account for the effect of the Sun.
This model has some families of lower dimensional tori, that gives
rise to a region of effective stablity at some distance of the
triangular points. It is remarkable that this region seem to persist
in the real system, at least for time spans of 1000 years.

This is a summary of the talk presented at the
V Jornadas de Mecanica Celeste, Albarracin, Teruel (Spain),
June 19--21, 2002.
