Transfers to Frozen Orbits Around Planetary Moons Using Manifolds of Averaged Dynamics

A novel methodology is proposed to design the transfers from halo orbits to low-eccentricity, high-inclination frozen orbits around planetary moons, with applications to the Jupiter-Europa system. The manifolds of averaged dynamics are used to reduce the transfer ΔV cost. A one-degree-of-freedom dynamical model around Europa, incorporating effects of Jupiter’s third-body perturbation and Europa’s nonspherical gravity, is established via double-averaging. Europa frozen orbits are calculated and classified into five groups according to their stability and locations in the phase space. The phase portraits indicate that low-eccentricity, high-inclination frozen orbits are always unstable, and manifolds are found to be associated with them. The transfers from halo orbits to these frozen orbits are designed by inserting into the manifolds first and then following the natural evolution until the arrival at the target frozen orbit. A nonlinear programming problem is established to optimize the transfers. Through the analytical derivations, the optimization model is simplified and finally solved by the particle swarm optimization algorithm. The efficiency of the proposed methodology is demonstrated by numerical experiments, which indicate that the transfer ΔV cost can be reduced by approximately 10 to 40% at the expense of longer transfer time.