  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.
