Measuring the Van Allen belts' radiation exposure for a spacecraft using low thrust systems

Abstract

The context of the problem studied is the transfer orbit of a spacecraft from a Low Earth Orbit(LEO) to outside Earth's Sphere of Influence using Solar Electric Propulsion (SEP), thus a lowthrust system. The specific impulse of this type of propulsion system is five to ten times greater thanthe one from ordinary chemical propulsion, which translates to higher efficiency. The followingoptimization problem can then be considered: finding positions and thrust arcs that maximize thefinal mass of the spacecraft for a given transfer orbit. However, the spacecraft must cross the VanAllen belts dozens of times during its trajectory due to its low thrust character, which poses ahazard to its electronic equipment due to the radiation exposure. Such trajectory passes through the belts, and their effect can be measured in a few ways: i) by the time the vehicle stays inside the belts; ii) by the integral of the density of particles in the corresponding time. The second option is more interesting, allowing us to develop a mathematical model of the density of particles with varying energies and with them calculate the total dose that will affect the spacecraft during the mission time. Using the results of thousands of simulations, it is possible to determine the dependency of the radiation dose with respect to the input parameters, such as the initial orbit and low thrust system characteristics. It is then of interest of the missionanalyst to optimize the final mass of the vehicle choosing the trajectory that satisfies the radiationlimitations, as well as minimizes the fuel consumption and transfer time.