In 1666 Isaac Newton proposed his universal law of gravitation. He considered a planet (mass m) moving in a circular orbit (radius r) at angular velocity w round the Sun (mass M)

Force on a planet
= F = mw^{2}r = mr(2p/T)
^{2} = 4p^{2}mr/T^{2}

Newton
assumed an inverse square law of force between the bodies, that is:

F = km/r^{2}
where k is a constant. The centripetal force formula gives:

F =
mv^{2}/r = km/r^{2 }= 4p^{2}mr/T^{2 }and so

T^{2} = 4p^{2}r^{3}/k and therefore
T^{2}/r^{3} is constant (and equal to 4p^{2}/k).

This shows that the inverse square law of force
is consistent with Kepler's third law.

We call Newton's constant (k)
the **universal constant of gravitation** and it is now written as G. The value of G has been found to
be 6.67x10^{-11} Nm^{2}kg^{-2}

For two spherical bodies with their centres separated by a distance d Newton's Law of universal
gravitation becomes: