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Calculate Orbital Angular Momentum

  1. Nov 2, 2011 #1
    Satellite of mass m is moving with velocity v in a circular orbit of radius r about mass M.

    Find the orbital angular momentum.

    Know

    [tex]v = \sqrt{\frac{GM}{r}}[/tex]

    Orbital angular momentum of a system is defined as the angular momentum of the center of mass of the system.

    Let the origin be at mass M.

    [tex]r_{cm} = \frac{m}{M + m} r[/tex]
    [tex]v_{cm} = \frac{v}{r} \frac{m}{M + m} r = \frac{vm}{M+m}[/tex]

    [tex]l = r_{cm} \times p_{cm} = (M + m) r_{cm} v_{cm} = \frac{m^2 rv}{M+m} = \frac{m^2}{m+M} \sqrt{GMr}[/tex]

    Correct answer in text is [tex]m \sqrt{GMr}[/tex]
     
  2. jcsd
  3. Nov 2, 2011 #2
    I think it is being assumed that M is MUCH bigger than m.
     
  4. Nov 2, 2011 #3
    Ok thanks, just wanted to be sure.
     
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