Mathematical Modeling of Solar Panel Temperature Dynamics in Various Conditions of Orbital Space Missions

The purpose of this research was to model the process of temperature changes on the spacecraft surface. First, we analyzed the angular distance from the Sun projection on the Earth's surface to the projection of the spacecraft orbit plane. Then, we estimated the borders of the shadow, half-shadow and illuminated areas of the orbits, as well as the borders of the long shadowless phase of spacecraft (SC) flight. As a result, we show the analysis of the shadowless SC flight phases for the several types of the orbits. According to the sources describing the calculation of the shadow and illuminated orbit areas, we found the factors that were not previously taken into account when determining the orbit area borders: the precession of the spacecraft orbit, the Sun ecliptic daily shift. Next, we identified the parameters required for calculating the light intensity of solar batteries. In this paper we present a model of the energy flow from the direct light flux reflected from the Earth, the radiant flux and self-radiation of the Earth under the changes in light intensity, the underlying surface, the terminator line position. Moreover, we give an example of calculating the solar panel temperature regime of the spacecraft located on the GLONASS system orbit on the half-shadow orbit area, the area with the mean value of the time spent in the shade, as well as the orbit area with the maximum value of the time spent in the shade. Finally, we show the results of solving the differential equation describing the heat exchange by radiation, by the trapezium method. As a result of our work, the method for calculating the temperature regime of the spacecraft surface was developed.

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