Determination of the Sun's and the Moon's sizes and distances: Revisiting Aristarchus' method

We have investigated the practicability of Aristarchus' method of determining the Sun's and the Moon's sizes and distances from Earth using a simple 8-in. telescope and a digital camera. Combining our astrometric observations made on October 20, 2012 with data from the lunar eclipse of June 15, 2011, and adopting a proper statistical approach, we obtain the two distances with errors of a few percent for the Moon and about 10% for the Sun. We also explain quantitatively why Aristarchus and his contemporaries, though able to measure the Moon's size and distance acceptably, could not be successful in determining the Sun's size and distance. Our experiment can be carried out in small semi-professional or amateur observatories and can be performed in an astronomy lab class.