What is Newton's gravitational constant mean?

[Max Born]

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.

 

[Ken G]

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.