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I Confusion about gravitational acceleration

  1. Jun 7, 2017 #1

    kmm

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    I understand that gravitational acceleration is independent of mass. However, I've seen a common mathematical description of this that I can't help but find circular. I suspect that there's an error in my thinking that I'm hoping someone can point out for me. It goes like this; ##F=mg## but we know that ##F=ma##. If we substitute the first equation into the second, we get ##mg=ma##, therefore ##g=a##. OK, but what seems wrong to me is that, once you state that the gravitational acceleration is the constant 'g', you're already saying it's independent of mass, BECAUSE it's a constant. And of course 'g' has to equal 'a' here; it is the acceleration. It seems to me that it's merely an experimental fact, so there's no need to justify it mathematically in this way. I feel like there's a subtlety I'm missing here.
     
  2. jcsd
  3. Jun 7, 2017 #2

    Dale

    Staff: Mentor

    This is correct. It is experimentally observed that the acceleration is independent of the mass. The form of the force law follows from that.
     
  4. Jun 7, 2017 #3

    kmm

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    Thanks, I wonder why some explain it in this way..
     
  5. Jun 7, 2017 #4

    Dale

    Staff: Mentor

    Well, the properties are encoded into the math so it is easy enough to start with the math and derive the properties
     
    Last edited: Jun 8, 2017
  6. Jun 7, 2017 #5

    russ_watters

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    Try deriving it from f=ma and Newton's law of gravity...
     
  7. Jun 8, 2017 #6

    kmm

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    Ok, in that case, we have $$ ma = G \frac {mM} {R^2}$$ so $$a = G \frac {M} {R^2}$$ which is independent of the mass 'm'. I guess deriving it from Newton's law of gravity, which is more general than the special case of 'f=mg', is actually bit more illuminating. Thanks
     
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