Thermal force effects due to the Earth infrared radiation acting on artificial satellites can explain most of the residual orbit decay observed on high altitude satellites. In this work, we propose an improved thermal model that presents the total thermal effect as a sum of the summer-winter and the "generalized" day-night effects. We show that a unified model may take into account the sin θ' term (where θ' is the co-latitude of the thermal energy source) for the day-night force component and the cos θ' term for the summer-winter force component. These terms are associated with temperature variations on the satellite's surface due to its movement around the thermal energy source and allow the simultaneous application of these two forces resulting in a unified total thermal force that has two components: the Summer-Winter force, in the satellite spin axis direction (z), and the generalized Day-Night force, in the satellite equatorial plane (xy). We calculate the along-track accelerations for a test-satellite (parameters based on the LAGEOS satellite data) and obtain the average along-track acceleration = -3.46 x 10 -13 ms -2 , for the day-night effect, and = -2.85 x 10 -12 ms -2 , for the summer-winter effect, that leads to a residual orbit decay of nearly 1.08 mmd -1 . Finally, we analyze the behavior of the average radial and along-track accelerations, and the thermal lag angle, as a function of the satellite's altitude, and show that there is a "selective law" that associates the maximum thermal effect to the radius and altitude of the satellite, and control the satellite orbit decay.
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
All bodies in the universe are constantly absorbing heat from surrounding thermal sources. This heat will be reemitted after a time lag. The temperature at each point of the heated surface will determine the frequency n of the photons sent out in such way that the total momentum associated to this process of energy loss depends on how the temperature is distributed at the surface. If the total momentum is not null, a thermal force will be produced whose intensity and direction will depend, fundamentally, on the temperature distribution at the surface: points with high temperature will re-emit photons with high frequencies and vice-versa. High frequency implies a great loss of momentum in the emission direction, and consequently great re-emission force in the opposite direction. But, not only the temperature can determine the frequency of the photons sent out but also the state at rest or movement of the body. When it presents some kind of movement (rotation, translation, etc.), the Doppler effect will change the frequencies of these photons and the frequency ν must be replaced by ν′. As a consequence, the resulting force will change too. In this work, we model the temperature variation (frequency variation) due to the Doppler effect and apply the new temperature distribution in the thermal re-emission model. The total force obtained by this "relativistic" thermal re-emission model has two terms: 1) the standard thermal re-emission force (without Doppler considerations) and 2) the relativistic correction of this force, similar to the standard Poynting-Robertson force. The thermal re-emission model presented here indicates that, in general, most of the several disturbing forces can be unified, providing a new and simple view for the understanding of the entire physics involved in such phenomena.Key words: Thermal re-emission; Poynting-Robertson; Doppler; Unified model; Non-gravitational effects. MODELO RELATIVÍSTICO DE RE-EMISSÃO TÉRMICA -
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