Abstract
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 ω 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 ω = 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 ω under consideration. Series of horizontal–critical periodic orbits of the short-Trojan families with the angular velocity ω and the mass ratio μ as parameters, are given.
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Papadakis, K.E. Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation. Astrophys Space Sci 299, 129–148 (2005). https://doi.org/10.1007/s10509-005-5158-8
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DOI: https://doi.org/10.1007/s10509-005-5158-8