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Gravitational fields

  1. Dec 9, 2013 #1
    1. The problem statement, all variables and given/known data

    What is the centripetal acceleration of a satellite orbiting Saturn at the location exactly one Saturn radius above the surface of Saturn

    2. Relevant equations
    In the previous question found out that the fg at that location is 1/4 of 36.0 N

    3. The attempt at a solution
    I read somewhere that they made centripetal acceleration equal to Gm/4pi ^2

    But why?? How are those two linked?
  2. jcsd
  3. Dec 9, 2013 #2

    rude man

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    I would not lend much credulity to what you read. The dimensions of Gm/4pi^2 are not the dimensions of acceleration.

    Equate gravitational acceleration to centripetal acceleration.
  4. Dec 9, 2013 #3
    The answer is the same as the gravitational intensity which is 2.60N . How does that work??
  5. Dec 9, 2013 #4

    rude man

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    Not too well. Acceleration is not measured in Newtons either ...
  6. Dec 9, 2013 #5
    Then how do u do this question?
  7. Dec 9, 2013 #6

    rude man

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    I have two masses m1 and m2. What is the (gravitational) force of m1 on m2 (or m2 on m1)?

    Picking the force on m2, then use F = ma on m2. Your answer is a. What is gravitational F?
  8. Dec 9, 2013 #7
    The mass being saturn's mass?
  9. Dec 9, 2013 #8
    Well, you have two masses to consider, the satellite's mass and Saturn's mass. After you make some cancellations in your equations, you may not need both values, though.

    Anyway, if this satellite is in orbit, it's experiencing a centripetal force. The real question: what force IS PROVIDING this centripetal force? What's the equation for this force that rude man is getting at? Equate this to your centripetal.
  10. Dec 9, 2013 #9
  11. Dec 9, 2013 #10

    rude man

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    How come three different masses?
  12. Dec 9, 2013 #11
    Oh no, the m in the first equation is the same as m1 in the equation after the equal sign.

    So when cancelled would be: v^2/r=Gm/ r^2?
    Last edited: Dec 9, 2013
  13. Dec 9, 2013 #12

    rude man

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    Looking better.
    So which is your m? The planet or the satellite? And what is r?
  14. Dec 9, 2013 #13
    Mass would be the mass of Saturn and radius would be the radius of Saturn *2? The thing is , all of this info is not given in the problem, so how are we supposed to know it?
  15. Dec 9, 2013 #14

    rude man

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    Take a trip to Saturn? Dunno, but you need both the mass and the radius of Saturn.
  16. Dec 9, 2013 #15
    i will try it out and see whether I can it.
  17. Dec 10, 2013 #16
    I tried it out and did not get the answer. Could it be any way that the gravitational field intensity is equal to the centripetal acceleration, since in the book, the answer to both is the same
  18. Dec 10, 2013 #17
    What's the book's answer? I was anticipating the reasoning you said you followed.

    Below I pulled Saturn's mass and radius from Google, thought if it's a book problem, I'm sure your text has similar values printed inside.

    mv^2/r = GmM/r^2
    v^2/r = GM/r^2
    where M = mass of saturn = 568.3 x 10^24 kg
    r = two saturn radii = 2(58,232,000 m)
    a = GM/r^2
    a = 2.79 m/s^2
  19. Dec 10, 2013 #18
    The answer is 2.60 m/s^2 which is the same as the gravitational intensity
  20. Dec 10, 2013 #19
    What is this gravitational intensity you keep bringing up?

    PS... I edited my post in the time you replied. I had made a calc error. I got a = 2.79 m/s^2, which is pretty close to 2.60m/s^2. I'm wondering if your book has different, perhaps rounded values for Saturn's mass and radius.
  21. Dec 10, 2013 #20
    This was a two part question. In the first it asked for gravitational intensity.
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