A simple numerical model for the variation of cubesat temperature along its orbit

Abstract

A simple model for the variation of CubeSat temperature along its orbit is presented. First, an analytic solution for the satellite temperature variation with time when subjected to a bistable heat source: two segments with piece-wise constant power, such as orbits with an eclipsed segment when the Sun is not directly visible, is considered. The model assumes that at a given time a single temperature applies to the entire satellite body. Discussion is focused on CubeSat satellites in low-Earth orbits, the uncertainties in predicted temperatures due to uncertain input parameters, and it emphasizes the importance of the satellite thermal inertia in setting the amplitude of the temperature variation along the orbit. This simplified “spherical cow" model is suitable for studying the relative effects of surfaces with different emissivities, the effects of small changes in the solar flux between June and December, the impact of thermal inertia, and as a “sanity check" for the results obtained with numerical thermal models that utilize detailed geometrical and thermal descriptions of all satellite components. It was found that the mean satellite temperature depends on the extreme values of steady-state equilibrium temperatures for eclipsed and non-eclipsed parts of the orbit, and the duration of the eclipse relative to the orbital period; in contrast, the amplitude of temperature variation around the mean temperature is by and large controlled by the satellite thermal inertia. A numerical model with arbitrary time dependence of the heating power is also developed, including its dependence on the satellite temperature, and validated it using analytic solution for a bistable heat source. Analysis of a typical 2U CubeSat shows that low temperatures are more worrisome than high temperatures, and that low temperatures can be mitigated by active temperature control such as releasing heat when the satellite is in eclipse using electrical energy stored in batteries that are charged during non-eclipsed portion of the orbit.