The stability of triangular libration points in the photogravitational three-body problem (Q2761348)

The author considers the motion of a passive gravitating particle \(P\) in the gravitational-repulsive field of two-radiating masses \(S_1\) and \(S_2\), revolving around one another in elliptic orbits. Like in the classical case, the libration points exist both in the circular and elliptic problems for any eccentricities. The author studies Lyapunov's stability of triangular libration points, and investigates the effect of eccentricities of the orbits of main bodies on the position and stability of these points. New instability zones are obtained, and it is established that this instability appears due to the parametric resonance, similarly as in the classical elliptic problem which is a particular case of the problem considered when the reduction coefficients are equal to 1.