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Homework Help: Calculating net gravitational force on the moon

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data

    The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force vector F SM that the sun exerts on the moon is perpendicular to the force vector F EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of earth = 5.98 1024 kg, mass of moon = 7.35 1022 kg. The distances shown in the drawing are rSM = 1.5 1011 m and rEM = 3.85 108 m. Determine the magnitude of the net gravitational force on the moon.

    2. Relevant equations
    F=G m1m2/r^2
    Fnet = √(F1^2 + F2^2)
    G = 6.674x10^-11

    3. The attempt at a solution
    For the force between the Sun and the Moon I got 4.04x10^20 and for the force between the Earth and the Moon i got 1.97x10^20 N and then for the net force I got 4.49x10^20 N

    I really don't know where I went wrong. I'm guessing my exponents are probably messed up? I've double and triple and quadruple checked it and I feel like my answer is right but WebAssign is saying I'm wrong. The calculations I used were

    F(Sun and moon) = (6.674x10^-11(1.99x10^30 x 7.35x10^22)/(1.55x10^11)^2
    Like I said, I got 4.04x10^20 N

    F(Earth and moon) = (6.674x10^-11(5.94x10^24 x 7.35x10^22)/(3.85x10^8)^2
    1.97x10^20 N

    Fnet = √((4.04x10^20)^2 + (1.97x10^20)^2)

    4.49x10^20 N

    Thanks for any help!
  2. jcsd
  3. Feb 11, 2014 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Welcome to PF!

    It looks like you used a slightly wrong value for the Sun-Moon distance in your calculation. Other than that, things look pretty good -- you are on the right track and your answer is not that far off.
  4. Feb 12, 2014 #3
    Thanks for pointing that out to me! I feel so dumb. Got the answer right!

    Thank you so much :)
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