On the existence of stable motions near the triangular points of the real Earth-Moon system

Angel Jorba, Dept. de Matematica Aplicada i Analisi, Universitat de Barcelona

In this talk we will focus on 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 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 ellipic ones give rise to a region of effective stablity 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.