EHFE refinement and extension for variable physical Earth radiation in spacecraft uncertainty thermal analysis

Spacecraft uncertainty thermal analysis is an important part of ensuring robust and reliable spacecraft thermal control system design. The calculation of the Earth external heat flux is an important part of it, however, the current model for calculating the Earth external heat flux is the constant physical Earth radiation model. In this paper, a model of the Earth's variable physical radiation is developed based on the long-term averaging method. We refine and extend the application of the external heat flux expansion (EHFE) formula to accommodate our proposed model. This study further includes an uncertainty analysis of Earth radiative external heat flux, utilizing the enhanced EHFE formula in the context of a representative spacecraft. We provide statistical data, such as mean values, standard deviation, and probability density functions, derived from our analysis. The augmented EHFE formula, when properly generalized, can be applied to compute the celestial body's variable physical radiative external heat flux affecting the spacecraft. This methodological advancement offers theoretical underpinning for the thermal design of spacecraft intended for deep space exploration.