Abstract
We report the results of detailed numerical calculations of the thermal thrust on the rapidly-spinning LAGEOS spacecraft. This thrust results from anisotropic emission of thermal radiation from its surface. LAGEOS is a good test case for such calculations because of its relatively simple structure and because precise orbit determinations based on laser ranging give observed thrust effects for comparison.
The numerical integration includes the varying heating over spacecraft-surface latitude from earth infrared radiation (for the earth-Yarkovsky force) and the varying solar heating as the spacecraft moves in and out of the earth's shadow (for the solar-Yarkovsky force). The computation allows for the poor thermal coupling between the spacecraft structure and individual surface elements (the fused-silica cube-corner reflectors and their aluminum retainer rings), and the poor conduction between structural hemispheres.
A Fourier analysis of the computed force with respect to orbital longitude gives the important frequency components for the computation of long-term orbit perturbations. Empirical formulas fit to the numerical results accurately express the component amplitudes as simple functions of spin axis orbital latitude, the sun aspect angle from the spin axis, and the fraction of the orbit period spent in the earth's shadow. These results. based on first principles, are similar to those from simplified theories of the thermal thrust. but add the following new feature: The decrease in orbit-averaged satellite temperature when the orbit intersects the earth's shadow decreases the earth-Yarkovsky drag by ∼ 0.14 pm/s2 from the no-eclipse value.
The development of spacecraft-element thermal parameters is the most difficult part of the analysis; the paper tabulates the parameters that should be directly measured before the launch of future geodynamic satellites.
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Slabinski, V.J. A numerical solution for lageos thermal thrust: The rapid-spin case. Celestial Mech Dyn Astr 66, 131–179 (1996). https://doi.org/10.1007/BF00054962
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DOI: https://doi.org/10.1007/BF00054962