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Biharmonic spline interpolation of spatial dose rate distribution in the minimum dose trajectory optimization problem

In this paper issues relating to geostationary orbit (GEO) insertion trajectory optimization is considered. The article discusses the GEO transfer trajectory optimization for a spacecraft with an electric propulsion (EP) system with the purpose of reduction of ionizing radiation dose absorbed by onboard systems from the Earth’s radiation belts. The considering trajectory optimization technique is based on the Pontryagin’s maximum principle and the method of numerical continuation. Much attention is paid to smooth approximation of the dose rate dependence on spatial coordinates using biharmonic splines interpolation. The proposed method makes it possible to abandon the methodological simplification of averaging the radiation dose rate over circular orbits to effectively solve this class of problems and directly consider the dependence of the dose rate on time and geographical longitude. Using as an example the minimum time problem for a test transfer, the errors in calculating the dose at the end of the transfer both by the proposed method and by the method of averaging over circular orbits are estimated. The proposed method turned out to be more than 13 times more accurate than the analogue. It can be applied in transfer trajectory optimization problems of an EP spacecraft in order to minimize the total accumulated ionizing radiation dose.