Fifth order solution of halo orbits via Lindstedt–Poincaré technique and differential correction method

Abstract

In the frame work of the perturbed restricted three-body problem, the solutions of halo orbits are developed up to fifth order approximation by using Lindstedt–Poincaré technique. The effect of oblateness of the more massive primary on the size, location and period of halo orbits around L1 and L2 are studied by considering the Earth–Moon system. Due to oblateness of the Earth, halo orbits around L1 and L2 enlarge and move towards the Moon. Also, the period of halo orbits around L1 and L2 decreases. Numerical solution for halo orbits around L1 and L2 in the Sun–Earth system is obtained by using the differential correction method for different values of radiation pressure and oblateness. The separation between the orbits obtained using fourth and fifth order Lindstedt–Poincaré method as well as differential correction method is found to be less than the separation between the orbits obtained using third and fourth order Lindstedt–Paincaré as well as differential correction method. This indicates that as the order of the solution increases the separation between consecutive solution decreases leading to more accurate solution.