# What is Newton's constant G?

Oct 5, 2017

G is the gravitational constant.

#### Explanation:

The universal law of gravitation says that the force of attraction between 2 bodies is proportional to the product of their masses, ${m}_{1} \mathmr{and} {m}_{2}$, 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.

$F = \frac{G {m}_{1} {m}_{2}}{r} ^ 2$

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:

$G = 6.67 \cdot {10}^{-} 11 N \cdot {m}^{2} \frac{\setminus}{\text{kg}} ^ 2$

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 $g = 9.81 m \frac{\setminus}{s} ^ 2$.

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

$g = \frac{G M}{r} _ {e}^{2} = 9.81 m \frac{\setminus}{s} ^ 2$

Where $M$ is the mass of the Earth and ${r}_{e}$ is the radius of the Earth.

I hope this helps,
Steve