Stability Zones Around the Triangular Lagrangian Points

Abstract

In the following we deal with the stability around the libration point L ₄ (respectively L ₅) in the circular restricted three body problem. The dependence of the largeness of the stability zones around these equilibrium points is established as a function of the mass parameter µ = m ₂/(m1 + m2) using extensive numerical experiments. The results are compared in a first step to existing ones of the Earth-Moon case (McKenzie and V.Szebehely, 1981) and then extended to different values of µ. The shrinking and even disappearance of such zones is well explained by the existence of 2 additional critical mass parameters well below the well known value of µ _crit = 0.03852... (A.Deprit and A.Deprit-Bartholomé, 1967).