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ay45c4-page12 - r r θ eθ r er\Centrifugal form of...

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Unformatted text preview: . . 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 71 ...
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