00-86 Jorba A.

A preliminary numerical study on the existence of stable motions near the triangular points of the real Earth--Moon system (955K, PostScript, gzipped and uuencoded) Feb 23, 00

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Abstract. Let us focus on the motion of an infinitesimal particle moving near the triangular points of the real Earth--Moon system. Here, by real Solar system we refer to the model defined by the well-known JPL ephemeris. It is known that, from a practical point of view, the neighbourhood of the triangular points is unstable, in the sense that nearby particles escape after a short period of time. In this paper we consider the existence of sets of solutions that remain near these points for a long time. To this end, we first use a simplified model (the so-called Bicircular Problem, BCP) that includes the main effects coming from Earth, Moon and Sun. The neighbourhood of the triangular points in the BCP model is unstable, as it happens in the real system. However, here we show that, in the BCP, there exist sets of initial conditions giving rise to solutions that remain close to the Lagrangian points for a very long time spans. These solutions are found at some distance of the triangular points. Finally, we numerically show that some of these solutions seem to subsist in the real system, in the sense that the corresponding trajectories remain close to the equilateral points for at least 1000 years. These orbits move up and down with respect to the Earth--Moon plane, crossing this plane near the triangular points. Hence, as it is discussed in the paper, the search for Trojan asteroids in the Earth--Moon system should be focused on these regions and, more concretely, in the zone where the trajectories reach their maximum elongation with respect to the Earth--Moon plane.

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