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.
Observational history of comets
Among the comets with short enough periods to have been observed several times in the historical record, Halley's Comet is unique in that it is consistently bright enough to be visible to the naked eye while passing through the inner Solar System. Since the confirmation of the periodicity of Halley's Comet, other [periodic comet]]s have been discovered through the use of the telescope. The second comet found to have a periodic orbit was Encke's Comet (with the official designation of 2P/Encke). During the period 1819–21 the German mathematician and physicist Johann Franz Encke computed the orbits for a series of comets that had been observed in 1786, 1795, 1805, and 1818, and he concluded that they were same comet, and successfully predicted its return in 1822. By 1900, seventeen comets had been observed through more than one passage through their perihelions, and then recognized as being periodic comets. , 305 comets have achieved this distinction, although several of these have disintegrated or been lost.