Formula omitted] and [formula omitted] axi-symmetric horseshoe periodic orbits about Lagrangian points: A global grid search approach

Abstract

This paper presents the numerical exploration of planar as well as spatial periodic horseshoe orbits about Lagrangian points in the framework of restricted three-body problem with radiation pressure and albedo as perturbations. The global grid search technique for obtaining both types of periodic horseshoe orbits is described. Further, several families of horseshoe orbits are obtained and then the orbital behaviour of each periodic orbit is investigated. By global grid search method, spatial axi-symmetric horseshoe orbits and their families are obtained via pseudo-arclength continuation. Interestingly, new forms of spatial horseshoe orbits are constructed and their orbital properties are analysed. Moreover, it is found that stable horseshoe orbits exists for different range of x0 in planar as well as in spatial case. Using parameter continuation, the effect of radiation pressure and albedo are discussed for the evolution of horseshoe orbits and found that the radiation pressure affects the shape of horseshoe orbits more then that of albedo. These results are helpful to analyse more generalized problem with other perturbations.