Swing-By Applications and Estimation of the Van Allen Belts’ Radiation Exposure for a Spacecraft in a Low Thrust Transfer to the Moon

This paper presents a handful of the underlying properties of a spacecraft’s transfer from a low Earth orbit (LEO) to the moon’s orbit using an electric propulsion (low-thrust) system. The use of analytical and numerical-analytical modeling in complex natural and technical processes is a key factor in this issue of Symmetry, which has been thoroughly explored in this paper. First, an optimization problem was considered to find the locations and lengths of the thrust arcs that maximizes the final mass of the spacecraft for a number of transfer orbits, thereby limiting the scope of trajectories to the most fuel-efficient ones. In addition to this, the Van Allen belts were modelled according to the density of electrons and protons in each point of space, in order to measure the total radiation absorbed by the spacecraft through an integration of the density of particles over the corresponding time. The simulations were then able to predict the relationship between the fluence of the particles and several initial parameters, such as the initial orbit’s eccentricity and the propulsion system’s characteristics. Then, a multi-linear regression and an artificial neural network were fitted to the data through a regression that related the fluence of protons and electrons as a function of the following parameters: mission time, specific impulse, thrust, final mass (i.e., propellant consumption) and the initial height of the perigee, eccentricity and inclination. This analysis was proven to be powerful due to the expressive values from statistical tests, showing underlying positive correlations between thrust, mission time and final spacecraft mass with the fluence of particles, and negative correlations between specific impulse, initial orbit eccentricity, inclination and the height of the perigee with the fluence of particles. Finally, an analysis of a swing-by maneuver was also carried out, together with the radiation incidence, revealing hidden dependencies of the increments in energy and velocity with respect to the fuel consumption, radiation absorption, propulsion system and initial orbit parameters