On the periodic motion in the photo-gravitational planar elliptic restricted four body problem

Since, orbital analysis in the vicinity of an equilibrium point of a dynamical system is a fundamental key to explore and understand about its dynamical behaviour. This paper contains orbital study of an infinitesimal mass under the frame of a photo-gravitational planar elliptic restricted four body problem (RFBP) in the context of long periodic and short periodic orbits near the equilibrium points in the presence of perturbation in the form of radiation pressure effect due to two primaries. The long periodic and short periodic orbits about each equilibrium points are obtained followed by the effect of radiation pressure force due to radiating primaries and impact due to variation of mass parameter are analysed. It is noticed that radiation parameter and mass parameter both have considerable influence on the orbital parameters (i.e. on the eccentricity, frequency, time period, semi-major and semi-minor axes) of the long as well as short periodic orbits near equilibrium points. To observe the nature of the orbits in the vicinity of respective equilibrium points, Poincaré surface of sections are estimated at different values of radiation parameter and mass parameter and then visualized the chaotic and quasi periodic nature of the orbits. These results will be helpful to study the more generalized problem with different kinds of perturbations.