This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a Sun-assisted low-energy trajectory is divided into three legs. Two interior legs, departing and arriving, are located inside the Earth–Moon region of prevalence and designed in the Earth–Moon circular restricted three-body problem, whereas the exterior leg lies outside the region of prevalence and is calculated in the Earth–Moon–Sun bicircular restricted four-body model. The whole trajectory is obtained by smoothly patching the three legs on the boundary of the region of prevalence. The arrival conditions are met by targeting a specific point in the L₂ lunar gateway. The interior legs are easily adjustable to the four-body dynamics. The database of planar lunar transfer trajectories can be used to select an initial guess for the multiple-shooting procedure of designing a three-dimensional Sun-assisted lunar transfer in high-fidelity dynamical models.

This paper explores the use of the averaging method in the optimal control problem related to the multirevolution orbital transfer of a spacecraft with low-thrust capabilities. The regularized equations of motion are expressed using modified equinoctial elements with the eccentric longitude as a fast variable. The control function is represented as a Fourier series relative to the eccentric longitude. The classical averaging technique’s usage results in the averaged trajectory depending only on a limited number of optimization parameters. Moreover, when transferring between near-circular orbits, the averaged motion can be estimated using analytical formulas. As such, the optimal multiorbit flight problem is simplified to nonlinear programming with fewer parameters, thereby accelerating the optimal solution’s derivation. Two practical examples illustrate the technique’s application: orbital transfer near the geostationary orbit and circular orbit raising maneuver. The solutions derived are compared with Pontryagin extremals.

Direct low thrust trajectory optimization techniques that reduce the optimization problem in the class of continuous functions to a nonlinear programming problem are described. Two direct low...

In September-October of 2021, the first student school on the interplanetary space mission analysis, design and optimization was initiated and hosted by Keldysh Institute of Applied Mathematics. The school objectives and format are presented and discussed in this preprint. The competition problem of designing a science mission to the Neptune system is described. The winner project is published to illustrate the level of the teams.