Unformatted text preview: T 2 a 3 = 4 Ï€ 2 GM tot 1.3.5 The virial theorem The virial theorem for one particle is: Â± m Â² v Â· Â² r Â² = 0 â‡’ Â± T Â² =1 2 Â± Â² F Â· Â² r Â² = 1 2 Â³ r dU dr Â´ = 1 2 n Â± U Â² if U =k r n The virial theorem for a collection of particles is: Â± T Â² =1 2 Âµ Â¶ particles Â² F i Â· Â² r i + Â¶ pairs Â² F ij Â· Â² r ij Â· 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: Â² F Â± = Â² FÂ² F app . The different apparent forces are given by: 1. Transformation of the origin: F or =m Â² a a 2. Rotation: Â² F Î± =m Â²Î± Ã— Â² r Â± 3. Coriolis force: F cor =2 m Â²Ï‰ Ã— Â² v 4. Centrifugal force: Â² F cf = m Ï‰ 2 Â² r n Â± =Â² F cp ; Â² F cp =mv 2 r Â² e r...
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 Spring '10
 Ye
 Force, Orbits, Conic section, Apparent Forces, virial theorem

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