  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.
