1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding equilibrium distance of an orbiting particle.

  1. Nov 21, 2013 #1
    1. The problem statement, all variables and given/known data

    In the diagram below, masses m and Me are in circular orbit about Ms with the same period.

    http://min.us/i/lprtU83D9cGR [Broken]

    Derive an expression for the equilibrium position r of mass m.

    2. Relevant equations

    For a circular orbit, the eccentricity, e = 0.


    Where [itex]h=\frac{L}{m}, k=-GMm[/itex]

    3. The attempt at a solution

    So, I'm kind of assuming that I simply set one of these equations to zero and solve for r, to get something like:

    [itex]r=\sqrt{\frac{-G^{2}M_{s}^{2}m}{2Ev^{2}}}[/itex] (which will not be imaginary because in an elliptical orbit E<0)



    Is it really that simple though? It's a 4 mark question.

    **EDIT** I think the above is wrong. I think I should have calculated the period of the mass m in terms of the two other masses, then equated it with the period of the other mass. I think I've got it now!
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 21, 2013 #2
    I would think that you need to consider the net force on mass m.
  4. Nov 21, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Sounds like you're finding Lagrange points. Are you told to assume m << Me << Ms?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted