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Weight planet problem

  1. Nov 17, 2012 #1
    1. The problem statement, all variables and given/known data

    A satellite of mass M = 683 kg is in circular orbit at height ho = 6.15x106 m above the surface of the Earth. Find:

    w, the weight of an astronaut of mass m = 75.5 kg inside the satellite.

    2. Relevant equations

    I believe it's something like:

    F = Gm_1*m_2/r²

    3. The attempt at a solution

    For the first part of the problem, I've found that the acceleration due to gravity is around 2.55 m/s².

    I used the form, but it's not right.

    F = 6.67 * 10^(-11) * 5.98 * 10^(24) * 75.5 / (6.15 * 10^(6) + 6.37 * 10^6)² ≈ 192 N
     
  2. jcsd
  3. Nov 17, 2012 #2
    If the satellite is in free-fall won't the astronaut weigh nothing?
     
  4. Nov 17, 2012 #3

    SammyS

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    You found the acceleration due to gravity. What is mass × acceleration due to gravity ?
     
  5. Nov 17, 2012 #4
    Then, it's just F = ma, and it becomes...

    F = 75.5 kg * 2.55 m/s²
    = 192.525

    However, the answer does not seem to be right. I don't get why this happens.
     
    Last edited: Nov 17, 2012
  6. Nov 17, 2012 #5

    SammyS

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    Do they mean apparent weight?
     
  7. Nov 17, 2012 #6
    Yes, I believe that is what the question is trying to ask! My instructor is not good in wording the question, so I got that part wrong.
     
  8. Nov 18, 2012 #7
    Actually, I need to find the weight of the astronaut IN the orbitting satellite!
     
  9. Nov 18, 2012 #8
    Wouldn't the astronaut weigh 0 N because it's in free fall as someone just said?
     
  10. Nov 18, 2012 #9

    haruspex

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    It depends what you mean by "weigh". If you stood the astronaut on a set of scales then yes, it would be 0. But if you mean the force exerted by gravity then your original answer is correct. In my view, the 0 answer comes about by using a non-inertial reference frame, which makes it as misleading as discussing centrifugal force.
     
  11. Nov 18, 2012 #10
    My original answer is correct if the question doesn't ask for apparent weight.

    BUT I am not sure if the answer is 0 or not. The astronaut is in the orbiting satellite.
     
  12. Nov 18, 2012 #11
    Haha. Very funny. Then, the answer is 0.
     
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