Due to its unique orbital characteristics, the retrograde geosynchronous orbit (RGSO) has demonstrated substantial potential in the fields of space surveillance and space situational awareness. However, constrained by the direction of Earth's rotation and the tracking, telemetry, and control capabilities of launch sites, the direct launch of satellites into RGSO from Earth must overcome an additional velocity increment of more than approximately 4 km/s, entailing enormous fuel consumption and significant engineering difficulty. Conventional approaches employ lunar gravity assists to transfer from low Earth orbit or geosynchronous transfer orbit to RGSO, yet the velocity increment requirements remain relatively high and the transfer paths are limited. With the increasing development of cislunar space in recent years, an increasing number of spacecraft on cislunar orbits are being launched and deployed. If a spacecraft is placed on standby in cislunar orbits, whether the sensitive dynamical characteristics of the three-body problem in cislunar space can be exploited to achieve low-energy transfer to RGSO has become a key issue for expanding the utilization value of cislunar space assets.
In a recent study published in Space: Science & Technology, researchers from Beihang University proposed a transfer path design method from cislunar orbits to RGSO. The study selects the distant retrograde orbit (DRO), as well as the L1 and L2 near-rectilinear halo orbits (NRHOs), as initial orbits. Within the framework of the bicircular restricted four-body problem (BCR4BP), a database search-based method combined with nonlinear programming optimization is employed to construct two-impulse and three-impulse transfer schemes, respectively. By identifying four transfer types—direct transfer, weak stability boundary (WSB) transfer, lunar gravity-assisted transfer, and their combinations—the study reveals the influence of different orbital reversal mechanisms—namely, apocenter reversal, solar gravitational exploitation, and lunar powered flyby—on fuel consumption. Simulation results demonstrate that three-impulse solutions can fill the gaps in the solution space of two-impulse solutions and optimize the Pareto frontier; the shortest transfer time can be achieved within 8 days, and the minimum fuel consumption is consistently below 1.5 km/s. After converting the four transfer types to the ephemeris model, direct transfers and lunar gravity-assisted transfers exhibit low sensitivity to the initial epoch, with feasible results obtainable for any initial epoch; weak stability boundary transfers feature two transfer windows per month, while the combined WSB-plus-lunar-gravity-assisted transfer, influenced jointly by the Sun–Moon phase, offers only one window per month. This study confirms the feasibility of deploying RGSO satellites from cislunar orbits, providing a new pathway to overcome the prohibitively high fuel consumption associated with direct launch from Earth.
First, this paper focuses on the transfer problem from cislunar orbits to retrograde geosynchronous orbits, and systematically presents the research background and dynamical model. Retrograde geosynchronous orbits possess unique orbital characteristics, enabling satellites to achieve rapid coverage of the geosynchronous orbital belt every 12 hours, which holds significant application potential in the fields of space surveillance and space situational awareness. However, constrained by the direction of Earth's rotation and the tracking, telemetry, and control capabilities of launch sites, the direct launch of satellites into RGSO from Earth must overcome a substantial additional velocity increment, resulting in prohibitively high fuel consumption. In recent years, the development of cislunar space has become increasingly active, and typical three-body periodic orbits in cislunar space—such as distant retrograde orbits and near-rectilinear halo orbits—have been incorporated into space mission planning. As shown in Fig. 1, the study establishes the dynamical model within the framework of the bicircular restricted four-body problem (BCR4BP), which assumes that the Earth and the Moon revolve in circular orbits around their barycenter, while the Sun moves in a coplanar circular orbit around the Earth–Moon barycenter. This model provides a closer approximation to the true ephemeris compared to the circular restricted three-body problem (CR3BP). Fig. 2 presents the three selected initial orbits: the 2:1 stellar-resonant distant retrograde orbit (the nominal orbit for NASA's Asteroid Redirect Mission), the L1 11:3 synodic-resonant near-rectilinear halo orbit, and the L2 9:2 synodic-resonant near-rectilinear halo orbit (the nominal orbit for the Lunar Gateway space station). The final target orbit is the retrograde geosynchronous orbit, with an altitude of 36,000 km, an inclination of 180°, and retrograde motion in the equatorial plane.
Second, this paper elaborates on the pulse transfer design method based on database search and optimization, and identifies four typical transfer types. The two-impulse transfer integrates forward from the cislunar orbit, establishes an initial guess database with departure point position, solar initial phase, and velocity ratio as search variables, and then employs nonlinear programming to optimize the total fuel consumption of the departure and insertion impulses. The three-impulse transfer adds a perilune impulse, constructs pre- and post-perilune Poincaré section sub-databases through forward and backward integration, respectively, and matches them to divide the transfer process into two segments for separate optimization, totaling three impulses. Fig. 3 presents the solution plane for two-impulse transfers from the distant retrograde orbit, with the horizontal axis representing transfer time and the vertical axis representing total velocity increment; red points denote direct transfers with apocenter altitude less than three times the Earth–Moon distance, while blue points denote weak stability boundary (WSB) transfers with apocenter exceeding three times the Earth–Moon distance. Direct transfers exhibit a semi-elliptical pattern, achieving orbital reversal through apocenter reversal; WSB transfers lift the apocenter to the weak stability boundary region, exploiting the sensitive solar gravitational dynamics to reduce perigee altitude, with transfer times exceeding 60 days but fuel consumption reduced to approximately 1.3 km/s. Fig. 4 illustrates the filling effect of three-impulse transfers (green and pink points) on the solution space of two-impulse transfers, where green points correspond to lunar gravity-assisted transfers, achieving orbital reversal through a powered flyby near the perilune and reducing total velocity increment to below 2.2 km/s for transfer times under 60 days; pink points correspond to combined WSB-plus-lunar-gravity-assisted transfers, further optimizing the Pareto frontier. For transfers from near-rectilinear halo orbits, three-impulse transfers similarly exhibit solution-space filling effects, with the shortest transfer time achievable within 8 days, and regardless of the initial orbit, the minimum fuel consumption consistently remains below 1.5 km/s.
Finally, this paper converts the typical transfer types to the ephemeris model to verify engineering feasibility, and analyzes the sensitivity of different transfer types to the initial epoch. A multiple shooting method is employed to transform the state vector from the Earth–Moon rotating frame to the Earth-centered J2000 inertial frame, while simultaneously accounting for the multi-revolution constraints of the initial orbit and the insertion constraints of the quasi-retrograde geosynchronous orbit. Fig. 5 presents the impulse variations for direct transfers under daily initial epochs in January 2025; the total velocity increment fluctuates by more than 100 m/s, while the transfer time varies within 1 day, and feasible results can be obtained for any initial epoch. Fig. 6 shows the results for weak stability boundary transfers under daily initial epochs in the first two months of 2025; the gray regions denote transfer failures or cases where the velocity increment exceeds the upper limit of 2 km/s, and owing to the solar phase influence, there are only two consecutive transfer windows per month. Fig. 7 presents the transfer windows for the combined WSB-plus-lunar-gravity-assisted transfer; there is only one window per month with a narrower duration, because this transfer is simultaneously influenced by the coupled Sun–Moon phase, and the specific Sun–Earth–Moon angular configuration occurs only once per synodic period of the Moon. Direct transfers and lunar gravity-assisted transfers exhibit low sensitivity to the initial epoch and high engineering feasibility, while WSB-type transfers are fuel-optimal but suffer from limited windows. This study confirms the feasibility of deploying retrograde geosynchronous orbit satellites from cislunar orbits, providing a new pathway to overcome the prohibitively high fuel consumption associated with direct launch into orbit.
