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r r θ eθ . r er \Centrifugal form of Pythagoras" We nd that the angular momentum equation is M 2 =
while the energy equation is
1 r_2 + r2_2 GM = M E = E :
The angular momentum equation can be interpreted geometrically
t + dt r(t + dt) dA d θ (t) t
r(t) In interval t to t + dt, the vector between the objects sweeps at area dA,
dA = 2 r rd :
Therefore, the rate of change of area is
dA = 1 r2_
which by the rst equation becomes
dA = 1 M L = L = constant.
dt 2 M1M2
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