Prior to the invention of the telescope many astronomers worked out theories of the motion of the Moon .
The purpose of such theories was to be able to predict the position of the Moon in the sky .
These geometrical models implied a certain range of distance of the Moon .
Ptolemy ’ s most quoted model , in fact , predicted that the Moon was nearly twice as far away at apogee than at perigee .
Measurements of the angular size of the Moon were within the capabilities of pre-telescopic astronomers .
These could have helped refine the models of the motion of the Moon , but hardly anyone seems to have made any measurements that have come down to us .
Using a piece of cardboard with a small hole punched in it which slides up and down a yardstick , we show that it is possible to determine an approximate value of the eccentricity of the Moon ’ s orbit .
On the basis of 64 observations taken over 14 cycles of the Moon ’ s phases we find \epsilon \approx 0.041 \pm 0.004 .
A typical measurement uncertainty of the Moon ’ s angular size is \pm 0.7 arcmin .
Since the Moon ’ s angular size ranges from 29.4 to 33.5 arcmin , carefully taken naked eye data are accurate enough to demonstrate periodic variations of the Moon ’ s angular size .