Phasing Maneuver Analysis from a Low Lunar Orbit to a Near Rectilinear Halo Orbit

The paper describes the preliminary design of a phasing trajectory in a cislunar environment, where the third body perturbation is considered non-negligible. The working framework is the one proposed by the ESA’s Heracles mission in which a passive target station is in a Near Rectilinear Halo Orbit and an active vehicle must reach that orbit to start a rendezvous procedure. In this scenario the authors examine three different ways to design such phasing maneuver under the circular restricted three-body problem hypotheses: Lambert/differential correction, Hohmann/differential correction and optimization. The three approaches are compared in terms of ΔV consumption, accuracy and time of flight. The selected solution is also validated under the more accurate restricted elliptic three-body problem hypothesis.

Method for calculating the perturbed trajectoryof a two-impulse flight between the halo orbit in the vicinity of the L2 point of the Sun — Earth systemand the near-lunar orbit

The paper introduces a new method for solving the problem of calculating the perturbed trajectory of a two-impulse flight between a near-lunar orbit and a halo orbit in the vicinity of the L2 point of the Sun — Earth system. Unlike traditional numerical methods, this method has better convergence. Accelerations from the gravitational forces of the Earth, the Moon and the Sun as point masses and acceleration from the second zonal harmonic of the geopotential are taken into account at all sections of the trajectory. The calculation of the flight path is reduced to solving a two-point boundary value problem for a system of ordinary differential equations. The developed method is based on the parameter continuation method and does not require the choice of an initial approximation for solving the boundary value problem. The last section of the paper provides examples and results of the analysis based on this method.