Thermal re-emission effects on the LAGEOS I satellite versus spin axis orientation

Abstract

Since 1976 when the LAGEOS I satellite was launched, the evolution of thermal re-emission effects has been observed and modeled. The effect of sun and earth heating has been analyzed separately and thermal models have been able, almost completely, to explain most of the residuals observed. However, after more than fifteen years of reasonable agreement between theory and observations, unexpected peaks in the along-track perturbations appeared and brought new attention to the problem of thermal force modeling. The efforts to explain these unexpected residual effects have produced interesting works such as the redefinition of the average coefficient of reflectivity (pressure of direct solar radiation), the Yarkovsky-Schach effect (thermal re-emission due to the solar heating), and the effect of asymmetrical reflection at the satellite's surface. Despite the lack of detailed data about the spin axis evolution, changes in the spin axis orientation have been also analyzed, however, none of these effects or corrections seems able to explain the observations. We present in this paper a unified thermal model that includes, simultaneously, the effects of sun and earth heating. The close connection between energy source coordinates (sun and earth) and the periodicity of satellite rotation and translation leads to complex sinusoidal functions that can explain the sudden peaks of maximum and minimum. We show that the residuals observed for LAGEOS I satellite can be predicted and explained by the thermal model presented and we also extend the analysis to a set of test-satellites with different spin axis inclinations concluding that the most stable spin axis configuration is the 90°-03°: spin axis perpendicular to the satellite orbital plane related to the Earth (90°) and spin axis lying on the orbital plane related to the Sun (03°). This configuration is desirable from the point of view of orbit stability because it minimizes the thermal re-emission effects and does not present great peaks of maximum after some years of orbit.Key words: Thermal Re-emission; Unified Model; LAGEOS. EFEITOS DE RE-EMISSÃO TÉRMICA NO SATÉLITE LAGEOS I VERSUS ORIENTAÇÃO DO EIXO DE ROTAÇÃO -Desde 1976, quando o satélite LAGEOS I foi lançado, efeitos de re-emissão térmica tem sido observados e modelados. Os efeitos de aquecimento devidos ao Sol e a Terra têm sido analisados separadamente e os modelos térmicos existentes têm revelado-se aptos a explicar, quase completamente, a maioria dos resíduos observados. No entanto, após mais de quinze anos de razoável concordância entre a teoria e as observações surgem picos inesperados nas perturbações transversais despertando renovada atenção ao problema da modelagem de forças térmicas. Os esforços para explicar esses efeitos residuais inesperados têm resultado em trabalhos interessantes assim como a redefinição do coeficiente de refletividade médio (pressão da radiação solar direta), o efeito