The effect of zonal harmonic coefficients in the framework of the restricted three-body problem

The objective of this paper is to present a comprehensive analytical study on the existence of the libration points and their linear stability in the frame of the restricted three-body problem considering the effect of the first two even zonal harmonics parameters with respect to both primaries. Moreover, the periodic orbits around the libration points, the expressions for semi-major and semi-minor axes, the eccentricities and the periods of elliptical orbits as well as the orientation of the principal axes are stated. In addition, we support our study with some numerical and graphical experiments.