Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon
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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BibTeX
@misc{caerols2026revisiting,
title = {{Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon}},
author = {Hugo Caerols and Martín Avendaño and Felipe A. Asenjo and Rafael Brahm},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28513},
eprint = {2609.28513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28513},
}
RIS
TY - UNPB
TI - Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon
AU - Hugo Caerols
AU - Martín Avendaño
AU - Felipe A. Asenjo
AU - Rafael Brahm
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.28513
UR - https://arxiv.org/abs/2609.28513
AB - 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.
ER -