Computation of three-dimensional periodic orbits in the sun-earth system

Abstract

In this paper, a third-order analytic approximation is described for computing the three-dimensional periodic halo orbits near the collinear L1 and L2 Lagrangian points for the photo gravitational circular restricted three-body problem in the Sun-Earth system. The constructed third-order approximation is chosen as a starting initial guess for the numerical computation using the differential correction method. The effect of the solar radiation pressure on the location of two collinear Lagrangian points and on the shape of the halo orbits is discussed. It is found that the time period of the halo orbit increases whereas the Jacobi constant decreases around both the collinear points taking into account the solar radiation pressure of the Sun for the fixed out-of-plane amplitude.