After comparing records of earlier comet sightings, Edmond Halley concluded that several appearances belonged to the same object. He predicted its return, and its later reappearance confirmed his prediction.
Halley's Comet orbits the Sun roughly every 76 years, although gravitational disturbances affect its period. It does not always return on the same date or in the same position.
Computation of orbit
Halley was the first comet to be recognised as periodic. Until the Renaissance, the philosophical consensus on the nature of comets, promoted by Aristotle, was that they were disturbances in Earth's atmosphere. This idea was disproven in 1577 by Tycho Brahe, who used parallax measurements to show that comets must lie beyond the Moon. Many were still unconvinced that comets orbited the Sun, and assumed instead that they must follow straight paths through the Solar System. In 1687, Sir Isaac Newton published his Philosophiæ Naturalis Principia Mathematica, in which he outlined his laws of gravity and motion. His work on comets was decidedly incomplete.
Although he had suspected that two comets that had appeared in succession in 1680 and 1681 were the same comet before and after passing behind the Sun (he was later found to be correct – see Newton's Comet), he was initially unable to completely reconcile comets into his model.
Ultimately it was Newton's friend, editor and publisher, Edmond Halley, who, in his 1705 Synopsis of the Astronomy of Comets, used Newton's new laws to calculate the gravitational effects of Jupiter and Saturn on cometary orbits. Having compiled a list of 24 comet observations, he calculated that the orbital elements of a second comet that had appeared in 1682 were nearly the same as those of two comets that had appeared in 1531 (observed by Petrus Apianus) and 1607 (observed by Johannes Kepler). Halley thus concluded that all three comets were the same object returning about every 76 years, a period that has since been found to vary between 72 and 80 years. After a rough estimate of the perturbations the comet would sustain from the gravitational attraction of the planets, he predicted its return for 1758. He personally observed the comet around perihelion in September 1682, but died in 1742 before he could observe its predicted return.
Halley's prediction of the comet's return proved to be correct, although it was not seen until 25 December 1758, by Johann Georg Palitzsch, a German farmer and amateur astronomer. Other observers from throughout Europe and its colonies sent confirmations to Paris after the comet brightened early the following year. In the Americas, John Winthrop lectured at Harvard University to explain the implications of the comet's reappearance for Newtonian mechanics and natural theology.
Another independent recognition that the comet had returned was made by the Jamaican astronomer Francis Williams, but his observations did not reach Europe. A unique portrait commissioned by Williams demonstrates the impact of the comet's return on period astronomers. Williams' hand rests on page 521 of the third edition of Newton's Principia with procedures to predict comet sightings. The white smudge in the sky is probably a depiction of Halley's comet relative to the constellations in March 1759, and the cord hanging above the book likely represents the comet's orbit. In 2024, using X-ray imaging, the painting was shown to depict the field of stars in which the comet would have been visible in 1759. Williams likely commissioned the portrait to commemorate his observations.
The comet did not pass through its perihelion until 13 March 1759, the attraction of Jupiter and Saturn having caused a delay of 618 days. This effect was computed before its return (with a one-month error to 13 April) by a team of three French mathematicians, Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute. The confirmation of the comet's return was the first time anything other than planets had been shown to orbit the Sun. It was also one of the earliest successful tests of Newtonian physics, and a clear demonstration of its explanatory power. The comet was first named in Halley's honour by French astronomer Nicolas-Louis de Lacaille in 1759.