There's an optical illusion known by names like the "lunar terminator paradox". This has much discussion and descriptions online, but none made sense in my head, so I wrote this program to figure out what was going on. The paradox: The moon is illuminated by the sun After sunset, the sun is below, so we would expect the illuminated portion of the moon to point down, towards where the sun is This isn't what always happens! I was camping in the mountains with a friend recently. We were looking up at the sky, just after the sun has set. The moon was clearly pointing up. After playing with this program , I have clarity: we're looking up at the moon from below. The most pathological case is a full moon. Let's say the moon is on the horizon: elevation=0. If we're looking at this low moon, and the moon is full, the sun is directly behind us. The moon is fully illuminated, and we see 100% of the moon disc lit up. Now, what happens if the moon is not at the horizon, but higher up at the sky?…