Calculating net gravitational force on the moon

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Homework Statement



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.



Homework Equations


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


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!
 

Answers and Replies

  • #2
Redbelly98
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Homework Statement



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.



Homework Equations


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


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!
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.
 
  • #3
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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.
Thanks for pointing that out to me! I feel so dumb. Got the answer right!

Thank you so much :)
 

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