Optimization Approach for Long-Lifetime Orbits Around Planetary Moons

High-inclination orbits around planetary moons often suffer from short lifetimes due to multiple perturbations. This paper proposes a novel methodology to achieve long-lifetime, high-inclination orbits around planetary moons. The methodology is based on the doubly averaged dynamics considering the nonspherical gravity of the moon and the third-body perturbation from the planet. A semi-analytical formulation for the estimated orbital lifetime is developed. With the maximization of the orbital lifetime as the objective, a nonlinear programming model is established and solved to obtain optimal initial conditions. Then, a numerical scheme, which is based on the golden-section search and the differential correction, is proposed to map the obtained initial conditions back to the unaveraged system, i.e., to the osculating elements. The effectiveness of the proposed methodology is demonstrated through its application to orbit design around several different planetary moons, and the underlying mechanism enabling long-lifetime orbits is also revealed. Results prove that the initial conditions yielding the longest orbital lifetimes reside on stable manifolds of equilibrium points, i.e., the frozen orbits. Moreover, some comparisons indicate that the proposed methodology can obtain significantly extended orbital lifetimes compared to those reported in prior studies.