J2 invariant relative orbits via differential correction algorithm

This paper describes a practical method forfinding the invariant orbits in J2 relative dynamics.Workingwith the Hamiltonian model of the relative motion includingthe J2 perturbation,the effective differential correction algo-rithm for finding periodic orbits in three-body problem isextended to formation flying of Earth’s orbiters.Rather thanusing orbital elements,the analysis is done directly in phy-sical space,which makes a direct connection with physicalrequirements.The asymptotic behavior of the invariant orbitis indicated by its stable and unstable manifolds.The periodof the relative orbits is proved numerically to be slightly dif-ferent from the ascending node period of the leader satellite,and a preliminary explanation for this phenomenon is pre-sented.Then the compatibility between J2 invariant orbit anddesired relative geometry is considered,and the design pro-cedure for the initial values of the compatible configurationis proposed.The influences of measure errors on the invariantorbit are also investigated by the Monte-Carlo simulation.