Dynamical Effects of Drag in the Circular Restricted Three-Body Problem: I. Location and Stability of the Lagrangian Equilibrium Points

Abstract The location and stability of the five Lagrangian equilibrium points in the planar, circular restricted three-body problem are investigated when the third body is acted on by a variety of drag forces. The approximate locations of the displaced equilibrium points are calculated for small mass ratios and a simple criterion for their linear stability is derived. If a1 and a3 denote the coefficients of the linear and cubic terms in the characteristic equation derived from a linear stability analysis, then an equilibrium point is asymptotically stable provided 0 -0.7265, the L4 point still exists and it is significantly less unstable than the L5 point. This provides a mechanism that would lead to a preference for objects at the L4 rather than the L5 point. Such a process may have implications for the origin and evolution of the Trojan asteroids and some of the smaller satellites of Saturn.