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r r θ eθ . r er \Centrifugal form of Pythagoras" We nd that the angular momentum equation is M 2 =
_
r
L= L
M1M2
while the energy equation is
1 r_2 + r2_2 GM = M E = E :
2
r
M1M2
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,
1
dA = 2 r rd :
Therefore, the rate of change of area is
dA = 1 r2_
dt 2
which by the rst equation becomes
dA = 1 M L = L = constant.
dt 2 M1M2
2
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This note was uploaded on 12/29/2011 for the course AST 350 taught by Professor Dion during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 dion

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