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Homework Help: Total Angular Momentum of A System

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Given the semimajor axis of Jupiter's orbit: 5.2 AU, and the eccentricity: .048 and the period: 11.86 years, find the total angular momentum of the Jupiter-Sun system. Assume it is an isolated system - ignore interactions from other planets etc.

    2. Relevant equations

    The first equation at the top of this page:http://en.wikipedia.org/wiki/Angular_momentum

    plus various geometric equations concerning ellipses.

    3. The attempt at a solution

    I wish I had one. My thought process is that I should find the angular momentum of each mass about the location of the center of mass which could be calculated easy enough. Since angular momentum is conserved, I can pick any arbitrary location and then calculate it. The problem I'm running into is mainly - assuming the above approach is correct - how to find the velocity of either Jupiter or the Sun at a given point on its orbit. With enough time perhaps I could derive an equation using Newton's universal gravitation law and what not, but I've been staring at this problem for a while and nothing is coming to me. Maybe my approach is inherently flawed...any help is appreciated. Thanks.

    edit: this is problem 2.6 in An Introduction to Modern Astrophysics, 2nd Ed.
  2. jcsd
  3. Jan 27, 2010 #2

    I think i've solved my original question, by using the formula L = u*sqrt(G*M*a(1-e^2)) where u is the reduced mass (m1m2)/(m1 + m2), G is the universal gravitation constant and M is the total masses m1 + m2 and finally since e=0, L=1.926E43.

    The next part of this questions asks what contribution the sun makes to the total momentum, assuming the orbital eccentricity of the sun is 0. My thought process is that since we can reduce our initial two body problem to simply the reduced mass orbiting about the COM which has mass M, I should be able to somehow "cut-out" the mass of the sun from the reduced mass and calculate it's angular momentum individually. All I would need to do is find the distance from the COM to the sun, and since I know it's period, I use the standard equation L=mrv and the answer should come right out. Is this the correct way of viewing the situation? If so, how do I find r? Every calculation I use factors in the reduced mass, but I don't think I want that...
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