Unformatted text preview: T 2 a 3 = 4 π 2 GM tot 1.3.5 The virial theorem The virial theorem for one particle is: ± m ² v · ² r ² = 0 ⇒ ± T ² =1 2 ± ² F · ² r ² = 1 2 ³ r dU dr ´ = 1 2 n ± U ² if U =k r n The virial theorem for a collection of particles is: ± T ² =1 2 µ ¶ particles ² F i · ² r i + ¶ pairs ² F ij · ² 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: ² F ± = ² F² F app . The different apparent forces are given by: 1. Transformation of the origin: F or =m ² a a 2. Rotation: ² F α =m ²α × ² r ± 3. Coriolis force: F cor =2 m ²ω × ² v 4. Centrifugal force: ² F cf = m ω 2 ² r n ± =² F cp ; ² F cp =mv 2 r ² e r...
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.
 Spring '10
 Ye
 Force, Orbits

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