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Total force on earth?

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the total force on the Earth due to Venus, Jupiter and Saturn, assuming all four planets are in a line (see figure).
    An amateur astronomer measures the masses to be MV = 0.888 ME, MJ = 324 ME, MS = 98.0 ME, and their distances from the Sun are 1.080×10^8 km, 1.500×10^8 km, 7.780×10^8 km and 1.430×10^9 km respectively.
    The mass of the earth ME is 5.980×10^24 kg and the distance from the earth to the sun is 1.500×10^8 km. The mass of the sun is 1.99×10^30 kg.


    2. Relevant equations
    F = Gm1 m2/r^2


    3. The attempt at a solution
    My problem is how to calculate the distance from each planet to earth. Like, if both Earth and Jupiter are 1.500x10^8 km from the sun, how far apart are they?
     
  2. jcsd
  3. Oct 29, 2012 #2
    so you've got five points on a line

    Sun Venus Earth Jupiter Saturn

    you know the distance from the Sun to each of these points

    From that you can know the distance between two of the points by subtracting the shorter distance from the longer one. For instance: the distance between Jupiter and Saturn would be found to be the distance from the Sun to Saturn minus the distance from Jupiter to Saturn.

    You might be able to see it more clearly if you draw out a picture of the situation. Don't worry about making it to scale.
     
  4. Oct 29, 2012 #3
    Okay, so:

    Distance from Earth to corresponding planet:

    Venus = 1.500×108 km - 1.080×108 km = 42,000,000 km = 4.2E10 m

    Jupiter = 7.780×108 km - 1.500×108 km = 628,000,000 km = 6.28E11 m

    Saturn = 1.430×109 km - 1.500×108 km = 1,280,000,000 km = 1.28E12 m

    F = GME[(.888ME/(4.2E102) + (324ME/(6.28E112) + (98ME/(1.28E122)]

    F = GME[(3010.3 + 4912.8 + 357.7)

    F = GME(8280.8) = 3.3E18 N

    ...but I still get the answer wrong. Any help? Would the force from Venus be negative because it's in a different direction than Jupiter and Saturn?
     
  5. Oct 29, 2012 #4
    haha answered my own question there - I set the (3010.3) to be negative and that gave me the right answer. Thanks for the help!
     
  6. Oct 29, 2012 #5
    btw for anyone wondering the correct answer is 9.03×10^17 N
     
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