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.

The work focuses on developing a lightweight lunar tug with an electric propulsion system for transporting cargo between promising near-Earth and near-lunar stations. The aim is to determine the ranges of transfer trajectory characteristics, considering realistic initial parameters: engine specifications, vehicle mass, launch date, and conditions. The lunar tug's design, solar panel parameters, and engine operating modes are provided. The flight scheme and method for designing transfer trajectories between near-Earth and near-Moon orbits are briefly described. The results of designing trajectories based on launch date, engine mode, and initial mass are presented and discussed.

In this paper, author proposes an approach to approximate orbital dynamics in the model of a perturbed Two--Body problem, which leads to a system of equations with a closed-form solution. The approach is based on representing the components of the disturbing acceleration by Fourier series in eccentric longitude with constant coefficients, writing out the equations of the perturbed two-body problem in terms of modified equinoctial elements, and averaging the right-hand sides of the equations of motion over the mean longitude on one orbit. It is discovered that the influence of disturbing acceleration on the resulting averaged equations can be parameterized by a finite set of scalar parameters, which are the coefficients of the Fourier series. Solutions of the averaged equations are found in a closed form in case of orbits with low eccentricity.