## Newton and universal gravity

Physics Narrative for 11-14

#### Newton's law

Newton's great achievement was to identify gravity as a force pulling objects (such as the infamous apple) to the ground and that this is the same force that keeps the Moon in orbit around the Earth, the Earth in orbit around the Sun, and so on. In other words, gravity is not some local force restricted to acting on the Earth but is a universal force which acts throughout the solar system and the universe.

Moreover, what Newton managed to do was to establish that the force depended directly on the masses of the objects involved and inversely on the square of the distance between them (as previously outlined). This he expressed mathematically in his universal law of gravitation, which states that:

The force which acts on mass *m* due to another mass *M*, a distance *r* away, is directed towards that second mass *M* and has a strength *F* which is given by:

force_{gravity} = *G* × *M* × *m*separation^{2}

Where G is the universal gravitation constant.

Notice that the gravitational force of one mass on another pulls from the centre of the first towards the centre of the second (and vice versa). Strictly speaking, Newton's equation applies to objects with spherically symmetric distributions of mass where *r* is the distance between their centres.