I should have mentioned that area = π r² is only an approximation for the moon’s apparent size in square degrees. What we really want to calculate is the surfac

I should have mentioned that area = π r² is only an approximation for the moon’s apparent size in square degrees. What we really want to calculate is the surface area of the spherical cap (on a unit sphere) with the same angular diameter as the moon. A formula for that is 2π(1 – cos r) [1], where r again is the radius of the moon in degrees. In this case, the two formulas give the same result to four significant digits (e.g. [2]). [1] https://en.m.wikipedia.org/wiki/Spherical_cap https://en.m.wikipedia.org/wiki/Spherical_cap [2] http://www.wolframalpha.com/input/?i=2pi%281-cos%5B%2834.1%2F60%2F2%29%2Api%2F180%5D%29%20steradians%20to%20square%20degrees http://www.wolframalpha.com/input/?i=2pi%281-cos%5B%2834.1%2...