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Three-body problem

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Three asteroids of masses M1 = 1.00 ×10^6 kg, M2 = 2.00 ×10^7 kg and M3 = 3.00 ×10^7 kg can be found at the positions r1 = (0, 0) m, r2 = (1 ×10^3, 0) m and r3 = (0, 6 ×10^2) m respectively. Calculate the resultant gravitational force on the asteroid of mass M1.



    2. Relevant equations

    F= (G m1 m2 m3 / r^2) r (this second r with a caret ^ and in bold type, thus being a unit vector)



    3. The attempt at a solution

    I'm usually pretty good at equations, but what has confused me is how to use the vectors in the equation. As i'm pretty sure the answer will require a vector which has a direction and magnitude, i'm not really sure where to begin with this one.
     
  2. jcsd
  3. Nov 30, 2011 #2
    Plot the asteroids on a coordinate system. Find the magnitude and direction of the gravitational forces from asteroids 2 and 3 on asteroid 1. Add the two vectors together to get resultant vector. Calculate magnitude and direction of resultant vector.
     
  4. Dec 1, 2011 #3
    Three Body Problem

    deleted
     
    Last edited: Dec 1, 2011
  5. Dec 1, 2011 #4

    Doc Al

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    Staff: Mentor

    Re: Three Body Problem

    No.

    First calculate the force that M2 exerts on M1. That will involve find the distance between them, but that's easily gotten from the coordinates without any calculation. Find the magnitude and direction of that force.

    Do the same for the force that M3 exerts on M1.

    Then add those two vectors to find the total force on M1.
     
  6. Dec 1, 2011 #5
    Re: Three Body Problem

    So, use the equation here? G m1 m2 / r^2 = force 1
    G m1 m3 / r^2 = force 2

    then force 1 + force 2?
     
  7. Dec 1, 2011 #6

    Doc Al

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    Staff: Mentor

    Re: Three Body Problem

    Yes. Where r is the distance between the masses.
    Yes, but you must add them as vectors. Direction matters.
     
  8. Dec 1, 2011 #7
    Re: Three Body Problem

    the distance between the masses only depends on m1 and m2, and then m1 and m3 right?

    And by adding the vectors, is this where i use pythagarus' therom?
     
  9. Dec 1, 2011 #8

    Doc Al

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    Staff: Mentor

    Re: Three Body Problem

    Right.
    Yes.
     
  10. Dec 1, 2011 #9
    deleted to clarify
     
    Last edited: Dec 1, 2011
  11. Dec 1, 2011 #10
    ok, redone my calcs, to get 5.7 x 10^-3
     
  12. Dec 1, 2011 #11
    Completed it, thanks guys!
     
    Last edited: Dec 1, 2011
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