20.2 The Distance to the Moon

The points AB are also located on another circle, centered on the Moon. The radius in that case is the distance R to the Moon, and because the arc AB covers 0.1 degrees, we get AB=2πr360×0.1

Strictly speaking, each of the two arcs AB expressed in the above equations is measured along a different circle, with a different radius (and the two circles curve in opposite ways). However, in both cases AB covers only a small part of the circle, so that as an approximation we may regard each of the arcs as equal to the straight-line distance AB. That assumption allows us to regard the two expressions as equal and to write 2πr360×0.1=2πr360×9

Multiplying both sides by 360 and dividing by 2π give 0.1R=9r⟹Rr=90 suggesting the Moon's distance is 90 Earth radii, an overestimate of about 50 per cent.