  In order to perform high resolution astrometry of the solar diameter from the
ground, through the observations of eclipses, the study of the limb darkening
profile is described. Knowing the profile of the solar limb is useful both to
monitor the solar radius over time, and to define the oblateness, which is
interesting for the classical tests of general relativity. The Limb Darkening
Function (LDF) is studied in order to find the inflexion point, to which the
measurements of the solar diameter are referred. The proposed method is applied
to the videos of the annular eclipse in January, 15, 2010. This new method
might solve the ambiguity of some eclipse obervations made with different
instruments, where the measured solar diameter was clearly dependent on the
aperture of the telescope and on the density of the filter used.
