Observational history of comets
Halley at first agreed with the longtime consensus that each comet was a different entity making a single visit to the solar system. In 1705, he applied Newton's method to 23 cometary apparitions that had occurred between 1337 and 1698. Halley noted that three of these, the comets of 1531, 1607, and 1682, had very similar orbital elements, and he was further able to account for the slight differences in their orbits in terms of gravitational perturbation by Jupiter and Saturn. Confident that these three apparitions had been three appearances of the same comet, he predicted that it would appear again in 1758–9. (Earlier, Robert Hooke had identified the comet of 1664 with that of 1618, while Giovanni Domenico Cassini had suspected the identity of the comets of 1577, 1665, and 1680. Both were incorrect.) Halley's predicted return date was later refined by a team of three French mathematicians: Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute, who predicted the date of the comet's 1759 perihelion to within one month's accuracy. Halley died before the comet's return; when it returned as predicted, it became known as Halley's Comet (with the latter-day designation of 1P/Halley). The comet next appears in 2061.
Oort cloud
There are two main varieties of short-period comet: Jupiter-family comets (those with semi-major axes of less than 5 AU) and Halley-family comets. Halley-family comets, named for their prototype, Halley's Comet, are unusual in that although they are short-period comets, it is hypothesized that their ultimate origin lies in the Oort cloud, not in the scattered disc. Based on their orbits, it is suggested they were long-period comets that were captured by the gravity of the giant planets and sent into the inner Solar System. This process may have also created the present orbits of a significant fraction of the Jupiter-family comets, although the majority of such comets are thought to have originated in the scattered disc.