Approximating elliptic halo orbits based on the variation of constants

A computational procedure is presented for approximating elliptic halo orbits about the collinear equilibrium points based on the variation of constants in the sense of the second-order approximation. Simulation results show that the approximate solutions agree well with the results of two-point boundary-value problems. The existence conditions of the elliptic halo orbits are also determined with respect to the mass ratio of the primaries and the eccentricity.