Radiation effect for a CubeSat in slow transition from the Earth to the Moon

A slow spiral transfer from the Earth to the Moon is calculated for the estimation of the total ionizing dose contributed from the Earth's radiation belts and energetic interplanetary solar protons. The Lagrange planetary equations are employed to calculate the evolution of the initial orbital parameters due to the thrust forces of the spacecraft. The trajectories from the equations are used for the numerical modeling of the populations of energetic particles in the radiation belts and interplanetary space. Transportation of these particles across model spacecraft indicated that an initial eccentric orbit, with periapsis and apoapsis corresponding to the low-altitude and geostationary orbit, slowly traverses the Earth's intense radiation belts. This traversal of the Earth's radiation belt dominantly determines the expected amount of ionizing dose with a significantly smaller contribution from the energetic solar protons. Several confidence levels for the numerical models are considered to provide statistical variations of the expected dose. The analysis, as applied to the recent mission concept of the lunar exploration with CubeSat, finds that substantial improvement of the current technology is still necessary in order to allow for the realization of this idea.