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Gravitational Law

  1. May 6, 2009 #1
    An object is fired vertically upwards from the surface of a planetary body; it moves under the action of Newton’s Gravitational Law, without
    resistance, so the equation is z'' = -gR^2 / (z + R)^2 . Find the relation between v = z' and z and use this model, and the relation that you have
    found, to obtain a numerical estimate for the escape speed on the surface of the Earth.

    What Ive done so far is transformed z'' to vz' using the chain rule.
    Next vz' = f(z)
    => 1/2*v^2 = int( f(z)dz + C )
    now solve v(z) = dz/dt
    => int (dt) = int(1/v(z)dz)
    So I got (gR^2)/(z+R) = (v^2)/2
    (2gR^2)/(z+R) = v^2

    This is where I got and I dont know where to go next, I dont even know if it's right? Could someone attempt this for me please? Thanks
     
  2. jcsd
  3. May 6, 2009 #2

    Cyosis

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    Homework Helper

    You arrived at the right expression, however you ignored the integration constant. How is z defined, is it the distance from the surface to the earth or from the center of the earth? Looking at your formula I would guess from the surface of the earth. This would give you a boundary condition v(0)=0.
     
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