Abstract
We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.
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Gaite, J., Sanz-Andrés, A. & Pérez-Grande, I. Nonlinear analysis of a simple model of temperature evolution in a satellite. Nonlinear Dyn 58, 405–415 (2009). https://doi.org/10.1007/s11071-009-9488-x
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DOI: https://doi.org/10.1007/s11071-009-9488-x