The Measurement of Solar Diameter and Limb Darkening Function with the Eclipse Observations

The Total Solar Irradiance varies over a solar cycle of 11 years and maybe over cycles with longer period. Is the solar diameter variable over time too? We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses by reconsidering the definition of the solar edge. A discussion of the solar diameter and its variations must be linked to the Limb Darkening Function (LDF) using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from satellite data. This approach unifies the definition of solar edge with LDF inflection point for eclipses and drift-scan or heliometric methods. The method proposed is applied for the videos of the eclipse in 15 January 2010 recorded in Uganda and in India. The result shows light at least 0.85 arcsec beyond the inflection point, and this suggests to reconsider the evaluations of the historical eclipses made with naked eye.