Halley's Comet - Computation of Orbit

Computation of Orbit

Halley was the first comet to be recognized as periodic. Until the Renaissance, the philosophical consensus on the nature of comets, promoted by Aristotle, was that they were disturbances in the Earth's atmosphere. This idea was disproved in 1577 by Tycho Brahe, who used parallax measurements to show that comets must lie beyond the Moon. Many were still unconvinced that comets actually orbited the Sun, and assumed they must instead follow straight paths through the Solar System.

In 1687, Sir Isaac Newton published his Principia, 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 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. This calculation enabled him, after examining historical records, to determine that the orbital elements of a second comet which had appeared in 1682 were nearly the same as those of two comets which had appeared in 1531 (observed by Petrus Apianus) and 1607 (observed by Johannes Kepler). Halley thus concluded that all three comets were in fact the same object returning every 76 years, a period that has since been amended to every 75–76 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.

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. It did not pass through its perihelion until 13 March 1759, the attraction of Jupiter and Saturn having caused a retardation of 618 days. This effect was computed prior to 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. Halley himself did not live to see the comet return, as he died in 1742. 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 his honour by French astronomer Nicolas Louis de Lacaille in 1759.

The possibility has been raised that 1st-century Jewish astronomers had already recognized Halley's Comet as periodic. This theory notes a passage in the Talmud which refers to "a star which appears once in seventy years that makes the captains of the ships err."