Abstract
A discussion of the solar diameter and its variations must be linked to the limb darkening function (LDF). We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses, using the luminosity evolution of Baily's Bead and the profile of the lunar edge available from satellite data. The method proposed is applied for the videos of the eclipse on 15 January 2010 recorded in Uganda and in India. We obtained a detailed profile constraining the inflection point position. The result suggests reconsidering the evaluations of the historical eclipses observed with a naked eye.
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