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Unformatted text preview: T 2 a 3 = 4 2 GM tot 1.3.5 The virial theorem The virial theorem for one particle is: m v r = 0 T =1 2 F r = 1 2 r dU dr = 1 2 n U if U =k r n The virial theorem for a collection of particles is: T =1 2 particles F i r i + pairs F ij r ij These propositions can also be written as: 2 E kin + E pot = 0 . 1.4 Point dynamics in a moving coordinate system 1.4.1 Apparent forces The total force in a moving coordinate system can be found by subtracting the apparent forces from the forces working in the reference frame: F = F F app . The different apparent forces are given by: 1. Transformation of the origin: F or =m a a 2. Rotation: F =m r 3. Coriolis force: F cor =2 m v 4. Centrifugal force: F cf = m 2 r n = F cp ; F cp =mv 2 r e r...
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 Spring '10
 Ye
 Force, Orbits

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