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**Unformatted text preview: **1.3.3 Gravitation The Newtonian law of gravitation is (in GRT one also uses instead of G ): F g =-G m 1 m 2 r 2 e r The gravitational potential is then given by V =-Gm/r . From Gauss law it then follows: 2 V = 4 G . 1.3.4 Orbital equations If V = V ( r ) one can derive from the equations of Lagrange for the conservation of angular momentum: L = V = 0 d dt ( mr 2 ) = 0 L z = mr 2 = constant For the radial position as a function of time can be found that: dr dt 2 = 2( W-V ) m-L 2 m 2 r 2 The angular equation is then: - = r mr 2 L 2( W-V ) m-L 2 m 2 r 2 -1 dr r-2 Feld = arccos 1 + 1 r-1 r 1 r + km/L 2 z If F = F ( r ) : L = constant, if F is conservative: W = constant, if F v then T = 0 and U = 0 ....

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