Nonlinear Stability of the Triangular Equilibrium Points in the Photogravitational Restricted Three-Body Problem When the Primaries are Oblate Spheroids

This study considers the framework of a planar Restricted Three-Body Problem (RTBP) in which both the primaries are oblate spheroids with their equatorial planes coincident with the plane of motion while the more massive primary is a source of radiation. The nonlinear stability of the triangular equilibrium points is investigated with the help of the mean motion derived by Sharma et al. [15] which is more accurate than the one used in earlier works. The Lagrangian of a third infinitesimally small body when it is near either of the triangular equilibrium points L₄/L₅ is formulated with respect to a synodic coordinate frame located at the respective equilibrium point. From the second order part of the Lagrangian, extracted using Taylor series expansion, second order part of the Hamiltonian of the system is derived and the equations of motion of the third body near the equilibrium points are obtained. Analyzing the characteristic equation of the system, which is similar for both the equilibrium points L₄/L₅, critical mass value that marks the linear stability of the triangular equilibrium points is obtained. Furthermore, Moser’s conditions are employed to find the two exceptional values of the mass parameter in the stable range at which stability cannot be guaranteed. By comparing with the results available in the literature, all three critical mass values are found to be lower than the values obtained for an ideal RTBP framework without oblateness or photo-gravitational effect. In addition to that, critical mass values are also affected due to change in the mean motion expression.