G is the planetary constant of attraction

No it's not. It's the universal gravitational constant. Nothing planetary about it. It's the constant of attraction between any two masses.

It's stupidly small, and has some totally daft units:

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

See:
http://scienceworld.wolfram.com/physics/GravitationalConstant.html