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.
Halley's Comet
Halley's calculations enabled the comet's earlier appearances to be found in the historical record. The following table sets out the astronomical designations for every apparition of Halley's Comet from 240 BC, the earliest documented widespread sighting. For example, "1P/1982 U1, 1986 III, 1982i" indicates that for the perihelion in 1986, Halley was the first period comet known (designated 1P) and this apparition was the first seen in half-month U (the second half of October) in 1982 (giving 1P/1982 U1); it was the third comet past perihelion in 1986 (1986 III); and it was the ninth comet spotted in 1982 (provisional designation 1982i). The perihelion dates of each apparition are shown. The perihelion dates farther from the present are approximate, mainly because of uncertainties in the modelling of non-gravitational effects. Perihelion dates of 1531 and earlier are in the Julian calendar, while perihelion dates 1607 and after are in the Gregorian calendar.