### Newton’s Law of Gravity

The current view of gravity in science is rather different to Newton's, but his theories and the mathematical relationship he gave are quite accurate enough for most situations.

Newtons view of gravity was as mutual attraction. He stated that the force of attraction was a property of all masses and that the larger each mass, the greater the force of attraction. A force of mutual attraction proportional to the product of the masses.

He explained that gravity is the force that maintains the orbit of moon around the earth, the planets around the sun. Before Newton no one had been able to explain the role of gravity in the rotation of the planets but Newton showed mathematically that the force of gravity obeyed the inverse square law (see video below).

He gave the relationship that

F = GMm/r2

Where M and m are the two masses and r is the distance between their centres. G is a constant of proportionality known as the universal gravitational constant.

He said that the gravitational field spread out as the distance increased, not in two dimensions but in three dimensions:

so using the example of the earth above, if we move to double the distance from the earth measured from the centre, the force of attraction is only a quarter, three times as far the force is then one ninth.

In this equation the value of G is tiny, 6.67408 ×1011 N⋅m2/kg2  so the force only becomes noticeable on our scale when the total mass is very large. The value of G was finely calculated in a number of practical experiments, one of the best known being by Henry Cavendish in 1798.