Discovery of Neptune
The planet Neptune was mathematically predicted before it was directly observed. With a prediction by Urbain Le Verrier, telescopic observations confirming the existence of a major planet were made on the night of September 23–24, autumnal equinox of 1846, at the Berlin Observatory, by astronomer Johann Gottfried Galle, working from Le Verrier's calculations. It was a sensational moment of 19th-century science, and dramatic confirmation of Newtonian gravitational theory. In François Arago's apt phrase, Le Verrier had discovered a planet "with the point of his pen".
In retrospect, after it was discovered, it turned out it had been observed many times before but not recognized, and there were others who made calculations about its location which did not lead to its observation. By 1846, the planet Uranus had completed nearly one full orbit since its discovery by William Herschel in 1781, and astronomers had detected a series of irregularities in its path that could not be entirely explained by Newton's law of universal gravitation. These irregularities could, however, be resolved if the gravity of a farther, unknown planet were disturbing its path around the Sun.
In 1845, astronomers Urbain Le Verrier in Paris and John Couch Adams in Cambridge separately began calculations to determine the nature and position of such a planet. Le Verrier's success also led to a tense international dispute over priority, because shortly after the discovery, George Airy, at the time British Astronomer Royal, announced that Adams had also predicted the discovery of the planet. Nevertheless, the Royal Society awarded Le Verrier the Copley medal in 1846 for his achievement, without mention of Adams. The Royal Society, however, also awarded Adams the Copley medal in 1848.
The discovery of Neptune led to the discovery of its moon, Triton, by William Lassell just seventeen days later.
Earlier observations
Neptune is too dim to be visible to the naked eye: its apparent magnitude is never brighter than 7.7. Therefore, the first observations of Neptune were only possible after the invention of the telescope. There is evidence that Neptune was seen and recorded by Galileo Galilei in 1613, Jérôme Lalande in 1795, and John Herschel in 1830, but none are known to have recognized it as a planet at the time. These pre-discovery observations were important in accurately determining the orbit of Neptune. Neptune would appear prominently even in early telescopes so other pre-discovery observation records are likely.Galileo's drawings show that he observed Neptune on December 28, 1612, and again on January 27, 1613; on both occasions, Galileo mistook Neptune for a fixed star when it appeared very close to Jupiter in the night sky. Historically it was thought that he believed it to be a fixed blue star, and so he is not credited with its discovery. At the time of his first observation in December 1612, it was stationary in the sky because it had just turned retrograde that very day. This meant that Neptune's motion was too slight to be detected at that date, and its apparent size was too small appear clearly as a planet in Galileo's small telescope. However, there is evidence that Galileo was aware there was something unusual about this "star". On January 28, Galileo recorded in his notebook that a background star had appeared to move, and drew Neptune's position with a dot in a different ink to the fixed stars. This suggests that Galileo had compared his 28 January observation to an earlier sketch drawn on the night of January 6, which would indicate a systematic search among his earlier observations. However, there is no clear evidence that he identified this moving object as a planet. Nor did he ever published these observations, or attempt to observe the moving source again.
In 1847, Sears C. Walker of the U.S. Naval Observatory searched historical records and surveys for possible prediscovery sightings of the planet Neptune. He found that observations made by Lalande's staff at the Paris Observatory in 1795 were in the direction of Neptune's position in the sky. In the catalog observations for May 8 and again on May 10 of 1795 a star was observed in the approximate position expected for Neptune. The uncertainty of the position was noted with a colon. This notation was also used to indicate an observation error so it was not until the original records of the observatory were reviewed that it was established with certainty that the object was Neptune and the position error in the observations made two nights apart was due to the planet's motion across the sky. The discovery of these records of Neptune's position in 1795 led to a better calculation of the planet's orbit.
John Herschel almost discovered Neptune the same way his father, William Herschel, had discovered Uranus in 1781: by chance observation. In an 1846 letter to Wilhelm Struve, John Herschel states that he observed Neptune during a sweep of the sky on July 14, 1830. Although his telescope was powerful enough to resolve Neptune into a small blue disk and show it to be a planet, he did not recognize it at the time and mistook it for a star.
Irregularities in orbit of Uranus
In 1821, Alexis Bouvard had published astronomical tables of the orbit of Uranus, making predictions of future positions based on Newton's laws of motion and gravitation. Subsequent observations revealed substantial deviations from the tables, leading Bouvard to hypothesize some perturbing body. These irregularities, both in the planet's ecliptic longitude and in its radius vector, could have been explained by several hypotheses: the effect of the Sun's gravity at such a great distance might differ from Newton's description; or the discrepancies might simply be observational error; or perhaps Uranus was being pulled, or perturbed, by an undiscovered planet.John Couch Adams learned of these irregularities while still an undergraduate and became convinced of the perturbation hypothesis. Adams believed that he could use the observed data on Uranus and Newton's law of gravitation to deduce the mass, position, and orbit of the perturbing body. After his final examinations in 1843, Adams was elected fellow of his college and spent the summer vacation in Cornwall beginning his calculations.
In modern terms, the problem is an inverse problem: an attempt to deduce the parameters of a mathematical model from observed data. Although the problem is a simple one for modern mathematics and electronic computers, at the time it involved much laborious manual calculation. Adams began by assuming a nominal position for the hypothesised body, using the empirical Bode's law. He then calculated the projected path of Uranus given the assumed position of the perturbing body and then computed the difference between his projected path and the recorded observations. He then adjusted the characteristics of the perturbing body based on these differences and repeated the process, essentially performing a regression analysis.
On 13 February 1844, James Challis, director of the Cambridge Observatory, contacted Astronomer Royal George Biddell Airy at the Royal Observatory, Greenwich, and requested data on the position of Uranus for Adams. Adams certainly completed some calculations on 18 September 1845.
Adams supposedly communicated his work to Challis in mid-September 1845, but there is some controversy as to how. The story and date of this communication only seem to have come to light in a letter from Challis to the Athenaeum dated 17 October 1846. However, no document was identified until 1904, when astronomer Ralph Allan Sampson found a note in Adams's papers that describes "the New Planet" and is endorsed, in handwriting that is not Adams's, with the note "Received in September 1845". Though this has often been taken to establish Adams's priority, some historians have disputed its authenticity on the basis that "the New Planet" was not a term current in 1845, and on the basis that the note is dated after the fact by someone other than Adams. Furthermore, the results of the calculations are different from those communicated to Airy a few weeks later. Adams certainly gave Challis no detailed calculations and Challis was unimpressed by the description of his method of successively approximating the position of the body, being disinclined to start a laborious observational programme at the observatory. Challis would ultimately remark that "while the labour was certain, success appeared to be so uncertain."
Meanwhile, on 10 November 1845, Urbain Le Verrier presented to the Académie des sciences in Paris a memoir on Uranus and showed that the pre-existing theory failed to account for its motion. Unaware of Adams's work, he attempted a similar investigation, and on 1 June 1846, in a second memoir presented to a public meeting of the Académie, he gave the position, but not the mass or orbit, of the proposed perturbing body. Le Verrier located Neptune within one degree of its discovery position.