Interplanetary Trajectory Design from a Moon-Grazing Retrograde Periodic Orbit around Earth

BERRETTI D. 1, OSHIMA K. 2

1 Politecnico di Milano, Milano, Italy; 2 Suwa University of Science, Chino, Japan

Deep-space missions that must depart Earth on short notice or with highly uncertain targeting, such as ESA’s Comet Interceptor, benefit from staging locations that reduce departure cost while preserving reasonable times of flight and flexibility in the achievable Earth-relative escape conditions. In this context, staging orbits such as Sun–Earth L2 (SEL2) orbits and near-rectilinear halo orbits (NRHOs) have emerged as attractive operational gateways, yet their relative performance depends strongly on how efficiently they can shape the outbound hyperbolic excess velocity. This work investigates a moon-grazing synodic resonant retrograde periodic orbit in the Earth–Moon environment as an alternative staging option. The orbit’s geometry naturally enables repeated interactions with the Moon over long durations, offering opportunities to retarget, rephase, and redirect departure conditions without large deterministic burns. This makes it a meaningful candidate for mission classes where adaptability and opportunity density can be as important as raw delta–v savings.

The purpose of the study is to assess whether this resonant retrograde periodic orbit is a competitive parking orbit for injections toward deep space. The analysis f irst characterizes the chosen orbit and assesses how efficiently the orbit can be accessed from Earth. It then focuses on how broadly and controllably it can deliver Earth-escape conditions in both magnitude and direction of the hyperbolic excess velocity, producing a systematic map of reachable escape conditions. In order to enable large-scale sampling, a patched-trajectory algorithm is developed to provide candidate trajectories from the parking orbit toward a prescribed Earth-escape condition, which are then optimized through a dedicated procedure using nonlinear programming. This is necessary to compare the orbit’s value as a staging location with established gateways such as SEL2. The final outcome is a set of design-oriented conclusions and guidelines on when this resonant option is advantageous.

The orbit family is reconstructed through continuation and differential correction, and its dynamical structure is quantified via stability and manifold analysis in the circular restricted three-body problem. Candidate Earth-access legs are obtained by targeted backward propagation around selected orbit phases, generating a structured catalogue of low-cost connections from the Earth vicinity. To evaluate departure performance, a database of orbit departures is generated by applying small impulsive perturbations and propagating for several weeks, generating multiple encounters with the Moon’s sphere of influence (SOI); these legs are then combined with Moon-to-Earth Lambert arcs to produce initial guesses that realize a wide range of outbound geometries. Each candidate is refined with constrained multiple-shooting and nonlinear programming, enforcing flyby consistency, operational bounds, and terminal escape conditions. The refined set is used to build reachability maps in Earth-centered excess velocity space and to extract design metrics that summarize maneuvering effort, timing flexibility, and sensitivity. A direct comparison with SEL2 is then enabled through a separate SEL2-to-deep space generation strategy based on manifold-informed initialization. The resulting reachability products are f inally interpreted in a mission context by linking admissible escape velocity vectors to families of heliocentric transfers relevant to Comet-Interceptor-like scenarios, providing a criterion to judge when the resonant RPO is advantageous relative to established staging orbits.