Aristarchos' Visual Minute
Aristarchos' 87 degrees may have come from the correspondence between 1 visual minute and a moon elongation of 6 degrees. (180º are to 6º what 30 visual minutes are to 1 visual minute). This correspondence is fairly close when the effect of the moon's daily wobble is taken into account. If the effect of air bending is also taken into account, then the correspondence becomes almost exact (as the reader may check by using this file)!
The closer the moon to the horizon, the greater the effect of air bending. The greatest distortion varies around a mean value of about 33'. How does this affect the shape of the moon's disc? How does the squashing affect the position of the moon's shadow line (or terminator) as seen (with the naked eye) from earth?