Measuring the Earth-Sun distance during a lunar eclipse

The classical method for measure the Earth-Sun distance is due to Aristarchus and it is based upon the measure of the angle Moon-Earth-Sun when the Moon is exactly in quadrature. Such an angle is only 9 arcminutes smaller than 90 degrees, and it is very difficult to evaluate, being necessary to look directly towards the Sun. The distance Earth-Moon and the Earth's diameter are necessary ingredients in order to derive the value of the astronomical unit. This method requires also the knowledge of the Moon's distance and the Earth's diameter, but it can permit a more precise measurement of the involved angles.