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What is Newton's gravitational constant mean?

  1. May 31, 2012 #1
    As the title already suggests, what does Newton's gravitational constant mean, and what it is, and how it is used in our universe?

    Hope you can help.
  2. jcsd
  3. Jun 1, 2012 #2

    Ken G

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    Gold Member

    Newton's gravitational constant is like any constant in physics that has units associated with it-- it is simply a reference situation in which the law applies, and as such is a conventional choice for making comparisons between different physical situations. Let me explain by rewriting the usual law of gravitational acceleration:
    g = GM/r2
    in a slightly different form:
    g/g0 = (M/M0)/(r/r0)2.
    Written in this better, but more longwinded form, we see that the law actually asserts a comparison between a general case, involving variables g, M, and r, with an arbitrarily chosen reference case, involving the subscript 0. I want to stress that we can choose any reference mass M0 and any reference distance r0 to measure our reference acceleration g0, and then just plug those reference values into the above equation. When we rewrite that equation in the first form, we see that
    G = g0 r02 / M0
    will result in the same value of G no matter what reference values we choose, but G will end up in different units if our reference units are chosen differently. That the reference situation is arbitrary is clear from that fact that we always have
    G = g r2 / M for any r and M and the g they produce. Hence the meaning of G is the statement that this combination of variables always comes out the same, and we can use any reference situation to determine its value.
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