How big is the Earth’s shadow on the Moon?

December 16, 2011 By: erik Category: Geeky, Math, Musings, Photos, Science

Earth's UmbraWhen I saw yesterday’s Astronomy Picture of the Day, I was fascinated by just how big the Earth’s shadow is on the Moon. When I made a comment to this effect on Facebook, my friend, Josh Grady, said, “It’d depend on the distance between the two, no?” Of course the size of a shadow depends on the distance to the object its cast upon, but I hadn’t considered that the distance from the Earth to the Moon varies, due to its slightly elliptical orbit around the Earth-Moon barycenter, by 42,840 km, causing it to appear 12% smaller at its apogee than at its perigee. This raised the question: What are the minimum and maximum sizes of the Earth’s shadow on the Moon?

To the geometrymobile!