Geometry of halo and Lissajous orbits in the circular restricted three-body problem with drag forces

Abstract

In this paper, we determine the effect of radiation pressure, Poynting-Robertson drag and solar wind drag on the Sun-(Earth-Moon) restricted three body problem. Here, we take the larger body of the Sun as a larger primary, and Earth+Moon as a smaller primary. With the help of the perturbation technique, we find the Lagrangian points, and see that the collinear points deviate from the axis joining the primaries, whereas the triangular points remain unchanged in their configuration. We also find that Lagrangian points move towards the Sun when radiation pressure increases. We have also analysed the stability of the triangular equilibrium points and have found that they are unstable because of the drag forces. Moreover, we have computed the halo orbits in the third-order approximation using Lindstedt-Poincar$\acute{e}$ method and have found the effect of the drag forces. According to this prevalence, the Sun-(Earth-Moon) model is used to design the trajectory for spacecraft traveling under the drag forces.