Linear approach to the orbiting spacecraft thermal problem

TL;DR

This paper introduces a linear perturbation-based method for solving nonlinear thermal equations in orbiting spacecraft, enabling efficient analysis of thermal modes and solutions, especially useful for reduced or conceptual models.

Contribution

It presents a novel linear approach using perturbation theory that decomposes thermal behavior into modes, improving computational efficiency over direct nonlinear integration.

Findings

The method accurately approximates the periodic thermal solution at second order.

It is computationally advantageous for reduced and conceptual thermal models.

The approach compares favorably with heuristic linearizations and direct numerical methods.

Abstract

We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. We apply our method to a minimal thermal model of a satellite with ten isothermal parts (nodes) and we compare the method with direct numerical integration of the nonlinear equations. We briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.