Multiobjective genetic optimization of Earth–Moon trajectories in the restricted four-body problem

In this paper, optimal trajectories of a spacecraft traveling from Earth to Moon using impulsive maneuvers (ΔV maneuvers) are investigated. The total flight time and the summation of impulsive maneuvers ΔV are the objective functions to be minimized. The main celestial bodies influencing the motion of the spacecraft in this journey are Sun, Earth and Moon. Therefore, a three-dimensional restricted four-body problem (R4BP) model is utilized to represent the motion of the spacecraft in the gravitational field of these celestial bodies. The total ΔV of the maneuvers is minimized by eliminating the ΔV required for capturing the spacecraft by Moon. In this regard, only a mid-course impulsive maneuver is utilized for Moon ballistic capture. To achieve such trajectories, the optimization problem is parameterized with respect to the orbital elements of the ballistic capture orbits around Moon, the arrival date and a mid-course maneuver time. The equations of motion are solved backward in time with three impulsive maneuvers up to a specified low Earth parking orbit. The results show high potential and capability of this type of parameterization in finding several Pareto-optimal trajectories. Using the non-dominated sorting genetic algorithm with crowding distance sorting (NSGA-II) for the resulting multiobjective optimization problem, several trajectories are discovered. The resulting trajectories of the presented scheme permit alternative trade-off studies by designers incorporating higher level information and mission priorities.     

Electrostatic particle collection in vacuum

Lunar grains accumulate charges due to solar-based ionizing radiations, and the repelling action of like-charged particles causes the levitation of lunar dust. The lunar dust deposit on sensitive and costly surfaces of investigative equipment is a serious concern in lunar explorations. Inspired by electrostatic precipitators (ESPs), the Electrostatic Lunar Dust Collector (ELDC) was proposed for collecting already charged lunar dust particles to prevent the lunar dust threat. As the conditions for terrestrial counterparts are not valid in the lunar environment, equations developed for terrestrial devices yield incorrect predictions in lunar application. Hence, a mathematical model was developed for the ELDC operating in vacuum to determine its collection efficiency. The ratios of electrical energy over potential energy, kinetic energy over potential energy and the ratio of ELDC dimensions were identified to be the key dimensionless parameters. Sensitivity analyses of the relevant parameters showed that depending on ELDC orientation, smaller particles would be collected more easily at vertical orientation, whereas larger particles were easier to collect in a horizontal ELDC configuration. In the worst case scenario, the electrostatic field needed to be 10 times stronger in the vertical mode in order to adequately collect larger particles. The collection efficiency was very sensitive to surface potential of lunar dust and it reached the maximum when surface potential was between 30 and 120 V.