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The force LRO experiences due to moons gravity?

  1. Mar 29, 2017 #1
    1. The problem statement, all variables and given/known data
    The Lunar Reconnaissance Orbiter (LRO) with mass m= 1850, maps the surface of the moon from an orbital altitude of 50 km. what are the magnitude and direction of the force the LRO experiences due to the moons gravity?

    2. Relevant equations
    Fg = (GMm)/r^2

    3. The attempt at a solution
    First I started by changing the units to SI
    Mass of moon M = .07x10^24 kg
    Mass of orbiter m = 1850 kg
    Gravitational constant = 6.637 x 10^-11

    the radius = (radius of moon + orbital altitude ) = 1.738 x 10^6 (value from my book) + 50,000 =
    1788000

    Now I just use the formula: [itex] F_g = (6.637x10^{-11})(.07x10^24)(1850) / 1788000^2 = 2688.478434 N [/itex]

    but my books answer is 2.83 x 10^3 N

    I don't understand what I did wrong as my answer comes from the formula... is there some trick im missing??
     
  2. jcsd
  3. Mar 29, 2017 #2

    mfb

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    Staff: Mentor

    You used the mass of Moon with one significant figure. Why do you expect your result to be accurate to more than that?
     
  4. Mar 29, 2017 #3
    I see what you mean. Does the method im using right though?

    Sucks that my book would give me mass that would give an inaccurate answer..
     
  5. Mar 30, 2017 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The method is fine.
    With a more precise mass for the Moon the answer will get closer to the book's answer.
     
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