Polar Ice Cap
Question: How much of the Earth's sunlight hits land under the icecaps?
First approximation: Circular Antarctica, no axial tilt
Antarctica is 14.6E6 km2, or 0.0286 of the earth's surface area AE = 5.1E8 km2 of the earth. We can approximate this as a circular cap with the northern edge at latitude \phi = 1.331 radians = 76.26°S . The cap area is A_C = 2\pi R^2(1-\sin(\phi)) , so we can compute the latitude of the cap from \phi = \sin^{-1}{ 1 - 2 A_C / A_E . The portion of the sun-facing disk occupied by this cap is 0.5 - ( \phi + 0.5 \sin{ 2\phi } / \pi
