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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, 1846, at the Berlin Observatory, by astronomer Johann Gottfried Galle (assisted by Heinrich Louis d'Arrest), 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 various 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 which could not be entirely explained by Newton's law of 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. Unfortunately, Le Verrier's triumph also led to a tense international dispute over priority, as, 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 discovery of Neptune led to the discovery of its moon Triton by William Lassell just seventeen days later.


Earlier observations

Neptune is invisible to the naked eye as it is too dim. 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 is 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 (in conjunction) 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; because it was only beginning its yearly retrograde cycle, Neptune's motion was thought to be too slight, and its apparent size too small, to clearly appear to be a planet in Galileo's small telescope. However, in July 2009 University of Melbourne physicist David Jamieson announced new evidence suggesting that Galileo was indeed aware that he had discovered something unusual about this star. Galileo, in one of his notebooks, noted the movement of a background star (Neptune) on January 28 and a dot (in Neptune's position) drawn in a different ink suggests that he found it on an earlier sketch, drawn on the night of January 6, suggesting a systematic search among his earlier observations. However, so far there is neither clear evidence that he identified this moving object as a planet, nor that he published these observations of it. There is no evidence that he ever attempted to observe it 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.