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Gravitational field strength

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Write an expression for the gravitational field strength E at a point distance r from a planet of mass M. (In my diagram, there are two planets with mass, m and distance 2a apart)

    2. Relevant equations



    3. The attempt at a solution

    The resultant gravitational field strength is towards the left. Using the parallelogram method to solve for the resultant vector and by the cosine rule,

    [tex]|E|^2=(\frac{GM}{R^2})^2+(\frac{GM}{R^2})^2-2(\frac{GM}{R^2})(\frac{GM}{R^2})\cos 120[/tex]

    [tex]|E|=\frac{GM\sqrt{3}}{(r^2+a^2)^2}[/tex]

    But the answer given is

    [tex]E=\frac{2GMr}{(a^2+r^2)^{\frac{3}{2}}}[/tex]
     

    Attached Files:

  2. jcsd
  3. Sep 16, 2010 #2
    I don't know what a parallelogram method is. You know from symmetry that the y components will cancel, so all you have to do is look at the two x components, which will both add to give

    2cosØ(GM)/(a^2+r^2)^(1/2), and cosØ=r/(r^2+a^2)
     
    Last edited: Sep 17, 2010
  4. Sep 17, 2010 #3
    Thanks for your help, Mindscrape!
     
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