Motion around the triangular equilibrium points of the restricted three-body problem under angular velocity variation

摘要

We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted three-body problem under the assumption that the angular velocity omega varies and for the Sun-Jupiter mass distribution. The symmetric periodic orbits emanating from the collinear Lagrangian point L-3, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value omega = 2 root 2 at which the triangular equilibria disappear by coalescing with the inner collinear equilibrium point L-1. We also compute the horizontal and the vertical stability of these families for the angular velocity parameter omega under consideration. Series of horizontal-critical periodic orbits of the short-Trojan families with the angular velocity omega and the mass ratio mu as parameters, are given.