The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L → . The magnitude of the areal velocity of the planet is :

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For small displacement d s of the planet its area can be written as d A = 1 2 r d l = 1 2 r d sin θ A.vel = d A d t = 1 2 r sin θ d s d t = V r sin θ 2 d A d t = 1 2 m V r sin θ m = L 2 m

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