Measuring the Earth-Sun distance during a lunar eclipse

TL;DR

This paper discusses a classical method to measure the Earth-Sun distance using lunar eclipses, focusing on the geometric angles involved and the necessary measurements of the Moon and Earth's dimensions.

Contribution

It revisits Aristarchus's method, emphasizing the potential for more precise angle measurements during lunar eclipses to determine the astronomical unit.

Findings

The angle Moon-Earth-Sun is approximately 9 arcminutes less than 90 degrees.

Precise measurement of involved angles can improve Earth-Sun distance estimates.

The method relies on known Earth and Moon dimensions.

Abstract

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.