althor wrote:The gravitational constant 'G' is just that, constant. Like e, pi, and others.
G = 6.67300 × 10 -11 m 3 kg -1 s -2.
g = (G * m1 * m2) / r^2
I was picking a nit and maybe it was uncalled for.
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I assume this would be the formula for determining the gravitational constant of any object... and thus G would actually vary per the formula based upon mass and radii of the object?
G is constant, which means it does not vary. At all. Ever. Well, not that we know of, anyway. But if we find some situation in which it changes we'll stop calling it a constant.
The gravitational attraction between two point
masses is the one given. Real objects, of course, are not point masses, so the way you actually have to calculate the gravitational attraction between them is to look at them as collections of tiny pieces, calculate the attraction between each pair of pieces, and sum them all together. Luckily, Sir Isaac Newton (and Gottfried Leibniz) devised mathematical tools that make summing infinite numbers of very small pieces easy[*]. Even better, it turns out that in the case of spherical objects we can just treat them as though they were both point masses located at their respective centers of mass, this is mathematically equivalent to the doing the infinite sum.
In the case of small masses (e.g. people) in relation to big masses (e.g. planets or moons), the fact that the small mass may not be spherical doesn't make enough difference to matter for practical purposes. Nor does the fact that planets and moons aren't truly spherical matter for most purposes (though it does matter for some!).
[*] EDIT: "easy" may be overstating the case. As anyone who's taken integral Calculus knows, integration can be easy, easy after a weird and often non-obvious transformation, or impossible (though numerical approximations are usually not too hard for a computer). But for nice, regular shapes like spheres, it's easy.
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