On the heat budget of the moon and the surface temperature variation during a lunar eclipse

Summary

The analysis of surface temperature variations of the moon is based on the equations of heat conduction and heat continuity in the interior of the moon andStefan's law. During a well-defined process, as exemplified by a lunar eclipse, the local heat budget equation establishes a boundary condition at the moon surface which must be satisfied by solutions of the thermal diffusion equation in the interior. Three simplified models of the general case are discussed. They are characterized by special assumptions regarding the depth and time dependency of the thermic qualities of the material underlying the moon's surface. In short, the thermal diffusivity is assumed to be constant in the first model, a linear depth function in the second and a time function in the third. A unique solution can be obtained for model No. I such that the absolute surface temperature is approximately inversely proportional to the 6th root of time during the phase of total eclipse.Epstein's conclusion that the average surface of the moon might consist of highly porous rocks or fine dust is confirmed by the order of magnitude of the heat conductivity which produces the best fit between the theoretical curves and a plot ofPettit's observational data during the lunar eclipse of 1939. Existing differences between the observed and theoretical curves during the totality phase of the eclipse can be reduced by the employment of the second model. A crude estimate shows that the average dust cover resting on more solid ground of lunar rocks might possibly have a thickness of approximately 0.5 meters.