What is Newton's constant G?

The universal law of gravitation says that the force of attraction between 2 bodies is proportional to the product of their masses, #m_1 and m_2#, divided by the square of the distance, r, between them. It is not equal to that, it is proportional to that.

So to get the the force of attraction #F# between 2 bodies in Newtons, you have to multiply by G.

#F=(Gm_1m_2)/r^2#

G has both a number as part of it and a combination of units. The constant G to make the formula come out in Newtons is:

#G = 6.67*10^-11 N*m^2 \/"kg"^2#

The units that are part of that constant are necessary to allow the units from the 2 masses and the square of the radius to be cancelled leaving Newtons as the only units on the result.

It is similar to the weight of a mass here on Earth. The weight is proportional to the mass. But, to get the weight in Newtons, you have to multiply by a constant of proportionality, which in that case is the acceleration due to gravity at the Earth's surface #g=9.81 m \/s^2#.

The acceleration due to gravity at the Earth's surface is given by:

#g = (GM)/r_e^2 = 9.81 m \/s^2#

Where #M# is the mass of the Earth and #r_e# is the radius of the Earth.

I hope this helps,
Steve