Lunar gravity assists (LGAs) are widely utilized in mission designs to potentially reduce transfer costs, particularly in noncoplanar cases requiring inclination adjustments. The commonly used patched-conic model and Keplerian map have low accuracy in designing close LGAs within the Earth–Moon system. Propagating LGA trajectories in the circular restricted three-body problem (CR3BP) offers higher fidelity but requires numerical integration. Therefore, a fast and accurate approach to estimate the state variation of the spacecraft after an LGA is significant. In this work, a 3-D LGA mapping in the CR3BP is studied, where deep neural networks (DNNs) are utilized to predict the state variation, gravity assist radius, and gravity assist type within a single orbital period. The LGA mapping is formulated with specific input and output parameters. The dynamical characteristics and data features resulting from the large mass ratio of the Earth–Moon CR3BP are analyzed. In particular, a small gravity assist radius causes significant perturbations to the Keplerian orbit, leading to abrupt local variations in the mapping outputs and challenges in sampling and fitting. To address this, a sampling approach based on the physical interpretation of the mapping inputs is proposed to improve the dataset, and a prediction framework combining classification and regression DNNs is employed. Test results demonstrate the efficiency and accuracy of the proposed DNNs-based LGA mapping, with average relative errors of 1.17% for state variation and 0.45% for gravity assist radius, and a 99.90% classification accuracy. In addition, the error distribution and extrapolation capability are evaluated and analyzed.

Abstract For BepiColombo's five-year journey into the inner solar system, a combination of low-thrust arcs and six flybys (one at Moon and Earth, two at Venus and two at Mercury) will be used to reach Mercury with low relative velocity. At arrival a gravitational capture approach is foreseen, in which the Sun perturbation is exploited to get weakly captured around Mercury for a number of orbits. This trajectory imposes severe constraints from a navigational point of view. Very precise navigation is required due to the low flyby altitudes planned for Venus (300 km) and Mercury (200 km) and the level of accuracy needed for the final arrival through the vicinity of the Sun–Mercury L1 point. Besides that, the solar plasma effect severely degrades the quality of the radiometric measurements near superior solar conjunctions, which are more frequent for missions to the inner solar system. Moreover, perturbations, as the ones introduced by momentum wheel desaturation burns, entry into safe modes or solar radiation pressure, must also be taken into account. Delta-differential one-way range measurements are found to be required in periods of poor orbit determination prior to some gravity assists. Nevertheless, if a safe mode is triggered at a critical moment that produces a change in velocity in an unfavourable direction, the mission could be jeopardised. To avoid that risk, an increase in the flyby altitude and possibly a partial or total redesign of the trajectory to avoid flybys nea

It is shown that the backward in time extension of the spacecraft interplanetary launch trajectory from the point of the low orbit of the departure planet generates a trajectory structurally coinciding with the virtual gravity assist trajectory near the departure planet. The pericenters of the auxiliary beam of the flying by hyperbolas and the time of their pericenter passage in this case differ slightly from the corresponding parameters of the designed departure orbit when starting from the specified point. Thus, the search for the trajectory of an interplanetary flight can be separated from the need to take into account the boundary conditions of the launch from an intermediate low pre-launch orbit. The pre-launch orbit is refined on the results of the search for the trajectory of the interplanetary flight. A structurally uniform scheme of ballistic design of spacecraft flight paths using multiple gravitational maneuvers based on the consideration of planetary ephemerides is presented.