Newton's Law of Gravitation

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 = mw²r = mr(2p/T) ² = 4p²mr/T²

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

F = km/r²     where k is a constant. The centripetal force formula gives:

F = mv²/r = km/r² = 4p²mr/T² and so
T² = 4p²r³/k and therefore T²/r³ is constant (and equal to 4p²/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 Nm²kg^-2

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