The moon orbits the earth - Leaving Cert Physics - Question b - 2009

This relationship can be expressed mathematically as:

$T^2 \propto R^3$

indicating that the period squared is proportional to the radius cubed.

For more precise calculations, this relationship can also be expressed as:

$T^2 = \frac{4\pi^2}{G M} R^3$

where G is the gravitational constant and M is the mass of the Earth.

In summary, the period of the moon's orbit increases with the radius of its orbit according to the cube root relationship, illustrating how larger orbits require longer periods to complete their revolution.