Physics planetary motion

Physics planetary motion - The motion of the Planets...

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1 The motion of the Planets See www.nasa.gov for more information Gravitational force 2 3 11 3 2 10 67 . 6 ˆ s kg m G r r mM G r r mM G F = = = r r Gravitational force is one of the four fundamental forces Simple case: motion in a central field (m<<M) r r mM G dt r d m r r 3 2 2 = Equation of motion Total energy is conserved r mM G mv E = 2 2 1 Angular momentum is conserved ) ( ) ( x y z z yv xv m v m r L = × = r r Properties of the motion in the central field Motion in a central field (m<<M) (cont.) 2 2 2 3 2 2 3 2 2 y x r y r M G dt y d x r M G dt x d + = = = Equation of motion in Cartesian coordinates Initial value ODE problem: equations + initial conditions (position and velocity) Motion in a central field (circular orbit) r v a 2 = For circular orbits 2 2 r mM G r v m = then … () 2 / 1 2 / 3 2 / 1 2 2 GM r v r T r M G v π = = = Motion in a central field (elliptical orbit) For circular orbits Properties: For any point on the elliptical orbit distance from F + distance form F’ = const
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This note was uploaded on 09/29/2009 for the course PHYSICS 811 taught by Professor Godunov during the Fall '09 term at Old Dominion.

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Physics planetary motion - The motion of the Planets...

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