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Gravitational Force Problem

  1. May 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Two asteroids are deep in space, far from any external influences. They each have a mass of 1010kg and are separated by distance L (center to center). They travel in a circular orbit around the center of mass of the system (radius of either orbit: R= 0.5L), under the influence of the force of gravitational attraction between them. If it takes either one of them 1 hr to make a full circle, what is their separation L?

    2. Relevant equations
    Possibly:

    F = GMm/r^2
    Fc = mv^2/r

    3. The attempt at a solution

    v = 2(pie)*r/(3600) = pie*L/3600

    Let F = Fc
    mv^2/r = Gmm/r^2
    v^2 = Gm/r

    r = 0.5L so:
    v^2 = Gm/0.5L
    I end up getting L = 0.1769m; however, the possible answers are:
    A) 675m
    B) 121m
    C) 1550m
    D) 60m
    E) 250m

    Thanks for the help
     
  2. jcsd
  3. May 4, 2009 #2

    LowlyPion

    User Avatar
    Homework Helper

    You have 2 different radii.

    The radius of rotation is about the center of mass. That is L/2.

    The radius of attraction for gravity is L.

    That means that

    mv2/(L/2) = GM2/L2

    v2 = GM/(2*L)
     
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