Jorba A.
A preliminary numerical study on the existence of stable motions
near the triangular points of the real Earth--Moon system
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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.