Newton's Principia and the theory of universal gravitation–Why Kepler did not apply to comets the laws of the planetary movements–Newton discovers the true system of cometary orbits–Halley and the comet of 1682; prediction of its return.

Kepler, in 1618, had already discovered the three laws upon which his fame rests, and which will render his name immortal. These laws govern the movements of bodies which, like the planets and the earth, revolve about the sun in regular periods. In virtue of the first law the orbit described about the sun is an ellipse, of which the sun itself occupies one of the foci; the second relates to the velocity of the planet, a velocity which is greater the nearer the planet is to the sun, and less in proportion as it is further removed; or more accurately the velocity is such that the areas of the sectors swept out by the radius vector of the planet are equal in equal times; hence it follows that the maximum of speed takes place at the perihelion, and the minimum at the aphelion. The third law expresses the constant relation which connects the duration of each periodic revolution with the longest diameter, or major axis of the orbit.