Limiting periodic orbits in the neighborhood of the triangular equilibrium points when the more massive primary is an oblate spheroid

In the restricted three–body problem, we explore the motion of the infinitesimal mass in the vicinity of the liberation point L4 taking into account the oblateness of the more massive primary. When higher order terms are retained in the analysis, the period of the orbit is found to be a function of the two finite masses and the size of the orbit. Furthermore, it is proved that the critical mass value decreases with oblateness. Finally, limiting periodic orbits are generated for values of the mass ratios 0.038097 and 0.038541. Both type of periodic orbits shift towards the smaller primary with oblateness. The effect is found to be more near the extreme of the major axes of the near-elliptical orbits with oblateness. Natural objects are frequently discovered circling near the Lagrange points of planetary systems due to the natural stability of L4 and L5. ’Trojans’ or ’Trojan asteroids’ are the generic names for the objects that inhabit those sites. As the Sun and Jupiter are the two most massive objects in the Solar System, there are more Sun–Jupiter Trojans than for any other pair of bodies. A space station could be placed in L4 or L5 of the Earth-Moon system in the future.