Gravitational Field Strength
A large stone experiences more force from the Earth. A small stone experiences less. In either case, it is really in the same field from the same Earth. To measure how strong the field is - on the Earth, on the moon, or far from either - we look at the force that acts on a body of the same mass, usually 1 kg.
This force per unit mass is called the gravitational field strength. It is given by g = F/m, where F is the force, and m is the mass of the stone. So g is the gravitational field strength.
Recall the the weight of the stone is given by Newton's law of gravitation, F = GMm/R2, where M is the mass of the Earth, m the mass of the stone, and R the distance from the centre of the Earth to the stone.
Therefore, the gravitational field strength at the stone is g = F/m = GMm/R2 / m = GM/R2.
The formula, g = = GM/R2, gives the gravitational field
strength around a body of mass M. The body can be a sphere, like a
ball or a planet. Then R is the distance from the centre of the
sphere to the point where we want to find the field strength.
Or, the body can be any shape, with a size much smaller than R.
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 25 September 2010.