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A numerical study on the existence of stable motions near the triangular points of the real Earth-Moon system
A dynamical systems approach to the existence of Trojan motions
Received 21 March 2000 / Accepted 18 September 2000
In this paper we consider the existence of stable motions for a particle near the triangular points of the Earth-Moon system. To this end, we first use a simplified model (the so-called Bicircular Problem, BCP) that includes the main effects coming from the Earth, Moon and Sun. The neighbourhood of the triangular points in the BCP model is unstable, as 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. These solutions are found at some distance from the triangular points.
Finally, we numerically show that some of these solutions seem to subsist in the real system (by real system we refer to the model defined by the well-known JPL ephemeris), in the sense that the corresponding trajectories remain close to the equilateral points for at least 1 000 years. These orbits move up and down with respect to the Earth-Moon plane, crossing this plane near the triangular points. Hence, 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.
Key words: celestial mechanics, stellar dynamics
© European Southern Observatory (ESO) 2000
Online publication: December 15, 2000