5.4.2 Newton’s law of gravitation

Newton's law of gravitation can also be described as a universal law of gravity. It describes the forces between any objects that have mass. The law can be used to explain motions such as the motion of planets round a sun, and why objects near the surface of the Earth will fall to the ground.

If we think about it, two objects m and M separated by a distance r will each create it's own gravitational field. The interaction of these fields gives rise to forces between the objects. According to N3 the objects must experience an equal and opposite force. Newton's law of gravitation states the force between two point masses is:

• directly proportional to the product of the masses, F ∝ Mm
• inversely proportional to the square of their separation, F ∝ 1/r².

From these statements we can create the equation:

F ∝ Mm/r²

The constant in this equation is known as the gravitational constant 'G'. This value is 6.67408 × 10^-11 m³ kg^-1 s^-2:

F = -GMm/r²

NOTE: we must use a minus sign as this shows that gravitational force is an attractive force. The attractive force (F) decreases with distance in an inverse-square relationship (F ∝ 1/r²) so doubling the distance will decrease the force by a factor of 4 (2²).

If several objects are involved the resultant force can be determined by vector addition.