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arXiv · 2609.28513

Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon

Hugo Caerols·Martín Avendaño·Felipe A. Asenjo·Rafael Brahm
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Abstract

In this article we revisit Aristarchus' ancient experiment to determine the ratios between the Earth-Moon and Earth-Sun distances. We present here the construction of a simple instrument, basically a tube that, by projecting its shadow, that allows one to estimate the Sun-Earth-Moon angle at the moment of first (or last) quarter. The simplicity of its construction and the accuracy of the measurements obtained may come as a surprise. We discuss the complexities involved in determining the exact moment of first quarter, based on the shape of the elliptical shadow projected on the Moon. Finally, we analyze and implement a strategy that allows us to approximate the measurement of this angle and estimate its value using observations that can be performed twice a month, and more accurately a couple of times during the year. We place Aristarchus' problem in its historical context and detail the physical and mathematical topics that can be developed and motivated through this experiment, in addition to carrying out a very thorough analysis of the errors associated with this measurement.

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Hugo Caerols, Martín Avendaño, Felipe A. Asenjo, Rafael Brahm. 2026-09-21. Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon. https://arxiv.org/abs/2609.28513

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