TITLE:
On 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 note we discuss the motion of a particle near the Lagrangian
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
show that trajectories with initial conditions in a vicinity of the
equilateral points escape after a short time. On the other hand, the
Restricted Three Body Problem is not a good model for this problem,
since it predicts a quite large region of practical
stability. Therefore, we introduce an analytic model that can be
written as a quasi-periodic perturbation of the Restricted Three-Body
Problem, that tries to account for the effect on the Sun and the
eccentricity of the Moon. Then, we compute some families of normally
elliptic 3-D invariant tori at some distance from the triangular
points, that give rise to regions of effective stability. By means of
numerical simulations, we show that these regions seem to persist in
the real system, at least for time spans of 1000 years.

This is a summary of a plenary talk at the Equadiff meeting held in
Hasselt, Belgium, July 22-26, 2003.