# Lunar Eclipse: Umbra and penumbra radii

**1. The problem statement, all variables and given/known data**

Find the radii of the umbra and penumbra circles drawn drawn perpendicular to the EMS axis, formed at a distance equal to that of the moon from the Earth.

**2. Relevant equations**

(From: http://ift.tt/1iWvvkX)

D2 / L1 = (P + U) / (L1 + L2)

D1 / L1 = P / L2

Total Shadow = 2P + U

D1 = Diameter of light source

D2 = Diameter of object between light source and Shadow

L1 = Length from light source to L1

L2 = Length from L1 to Umbra

U = Umbra

P = Penumbra

**3. The attempt at a solution**

I substituted 12,576 km for D2 as the diameter of earth and 149.6 million km for the distance between the earth and sun. My calculations revealed that P+U= 1305010.784. Am I misguided in the belief that these equations give my the area of the circles from which I can extrapolate the radii?

http://ift.tt/1iWvvl1

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