# Mechanics and gravitation

### Isaac Newton

#### Mechanics and gravitation

According to the well known story, it was on seeing an apple fall in his orchard at some time during 1665 or 1666 that Newton conceived that the same force governed the motion of the Moon and the apple. He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and the problems of planetary motion.Correspondence with Hooke (1679 1680) redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance, he determined it to be an ellipse, so informing Edmond Halley in August 1684. Halleys interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write the Principia.

Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centres of force. Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles.Book II inaugurates the theory of fluids. Newton solves problems of fluids in movement and of motion through fluids. From the density of air he calculated the speed of sound waves.Book III shows the law of gravitation at work in the universe. Newton demonstrates it from the revolutions of the six known planets, including the Earth, and their satellites. However, he could never quite perfect the difficult theory of the Moons motion. Comets were shown to obey the same law, in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter, already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation.

Newtons work in mechanics was accepted at once in Britain, and universally after half a century. Since then it has been ranked among humanitys greatest achievements in abstract thought. It was extended and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into the late 19th century before it began to show signs of failing. See Quantum Theory, Relativity.