Effect of perturbations in the Coriolis and centerifugal forces on the locations and stability of the equilibrium points in Robe's circular problem with density parameter having arbitrary value. (Q1411772)

The authors study the effect of perturbations in Coriolis and centrifugal forces on the locations and linear stability of equilibrium points in Robe problem. On the line joining the centers of the first and second primaries, there is an equilibrium point for all values of \(K\) except \(K=1+2\mu\), where \(\mu\) is the mass parameter. There is on this line a second equilibrium point only when \(K>1\). When \(K<0\) and \(K+\mu>0\), there are two equilibrium points in the \(z\)-\(z\)-plane, equidistant and forming triangles with the line joining the centers of the first and the second primaries. When \(K=(1+s')(1-\mu)\), there are an infinite number of equilibrium points in the \(x\)-\(y\)-plane lying in a circle with center at the second primary and having radius \(1-\frac12 s'\). Further, the authors prove that the circular and triangular equilibrium points are always unstable. They also consider certain conditions on \(K\) and \(n\) which satisfy the equilibrium points collinear with the center of the first and second primaries in order to be stable.