Estimation of solar illumination on the Moon: A theoretical model

The solar illumination conditions on the lunar surface represent a key resource with respect to returning to the Moon. As a supplement to mapping the solar illumination by exploring data, lighting simulations using high-resolution topography could produce quantitative illumination maps. In this study, a theoretical model is proposed for estimating the solar illumination conditions. It depends only on the solar altitude and topographical factors. Besides the selenographic longitude and latitude, the former is determined by the selenographic longitude and latitude at the subsolar site, the geocentric ecliptical latitude, and the dimensionless distance of the Sun–Moon relative to 1 AU, which are function of time. The latter is determined by comparing the elevations in solar irradiance direction within 210 km in which the topography might shadow the behind sites to the critical elevations determining whether the behind sites are shadowed or not. Compared to Zuber's model, the model proposed in this study is simpler and easier for computing. It is parameterized with selenographic coordinates, elevations, and time. With high-resolution topography data, the solar illumination conditions at any selenographic coordination could be estimated by this model at any date and time. The lunar surface is illuminated when the solar altitude is non-zero and all the elevations within 210 km in solar irradiance direction are lower than the critical elevations. Otherwise it would be shadowed.