In reply to:

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[G is] stupidly small, and has some totally daft units:

G = 6.672x10^-11 N m^2 kg^-2

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Au contraire, the units make a lot of sense. The force is proportional to the product of the two masses you're considering, and inversely proportional to the square their separation. So, multiply G by two masses (kg^2) and divide it by the square of the distance (m^-2), and lo&behold, you end up with a number of newtons - just as you'd expect for a force.

Dimensional analysis, lesson one.