The size of the shadow can be determined with one of the long lost rules in geometry: the center of a circle can be identified using two chords on the circle. Simply draw two (or more) chords on a circle. Next, draw a line at the mid-point of a chord that is perpendicular to the chord. Repeat this procedure for a second chord. The intersection of the perpendicular lines marks the center of the circle. And, knowing the position of the center of the circle, the radius (and thus the diameter) of the circle can be easily measured.
Perform this procedure on the portion of the shadow that can be seen against the background of the Moon. Then, measure the diameter of the Moon from the same image, and compare the size of shadow with the size of the Moon.
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