A Mixture of Ancient and Modern Understanding Concerning the Distance and Motion of the Moon

TL;DR

This study analyzes naked eye observations of the Moon's size over time, revealing regular variations that challenge ancient models and align with modern understanding of orbital mechanics and perturbations.

Contribution

It demonstrates that ancient astronomers could have identified flaws in Ptolemy's model through simple observations, and explains modern causes of lunar distance variations.

Findings

Observed lunar size variations of at least 3 arc minutes.

Correlated lunar anomalies with phase and orbital effects.

Challenged ancient assumptions with empirical data.

Abstract

Ptolemy's model of the Moon's motion implied that its distance varies by nearly a factor of two, implying that its angular size should also vary by nearly a factor of two. We present an analysis of 100 naked eye observations of the Moon's angular size obtained over 1145 days, showing regular variations of at least 3 arc minutes. Thus, ancient astronomers could have shown that a key implication of Ptolemy's model was wrong. In modern times we attribute the variation of distance of the Moon to the combined effect of the ellipticity of the Moon's orbit and the perturbing effect of the Sun on the Earth-Moon system. We show graphically how this affects the ecliptic longitudes and radial distance of the Moon. The longitude and distance "anomalies" are correlated with the Moon's phase. This is illustrated without any complex equations or geometry.