how Neptune was discovered by math

The Mechanism

Uranus, discovered by William Herschel on 13 March 1781, refused to keep to the orbit that Newton's laws predicted for it. By the 1820s and 1830s the residuals — the difference between where Uranus was in the sky and where it should be — had grown to more than two arcminutes, forty times any plausible measurement error. Either Newton was wrong at solar-system scale, or another planet, unseen, was pulling on Uranus from beyond. In September 1845 a 26-year-old Cambridge fellow named John Couch Adams (born 5 June 1819 at Lidcott Farm, Cornwall; senior wrangler at St John's College 1843) submitted to Sir George Airy, Astronomer Royal, a set of hand-computed orbital elements for a hypothetical trans-Uranian planet. Airy — the head of Greenwich Observatory and one of the most powerful figures in British science — filed the paper and did nothing with it for eight months. In parallel, at the Bureau des Longitudes in Paris, a 35-year-old French mathematician named Urbain Jean Joseph Le Verrier (born 11 March 1811 in Saint-Lô, Normandy) had been assigned the same problem by François Arago. Le Verrier worked in near-total isolation for a year and a half, publishing three memoirs — 10 November 1845, 1 June 1846, and 31 August 1846 — in the *Comptes rendus* of the French Academy of Sciences. In the third of them he gave a specific predicted position: right ascension 326°32' in the constellation Aquarius, mean distance from the Sun about 36 astronomical units, mass a little larger than the Earth. On 18 September 1846 Le Verrier, frustrated that no French astronomer would take him seriously, wrote personally to Johann Gottfried Galle (born 9 June 1812 in Radis, near Wittenberg) at the Berlin Observatory. "Direct your telescope," the letter said, "at a point on the ecliptic in Aquarius, in longitude 326°, and you will find within a degree of that place a new planet, of appearance about a star of the ninth magnitude, and having a perceptible disc." The letter arrived at the Berlin Observatory on the evening of Wednesday, 23 September 1846 — Galle's birthday. Galle showed it at once to the Observatory director, Johann Franz Encke, who agreed to let him look that night. Galle's young assistant, Heinrich Louis d'Arrest, then 24, suggested checking the region against a fresh, still-unpublished star chart — Hora XXI of the Academy Star Charts series — that the Observatory had just received from its cartographer Carl Bremiker. At the 9-inch Fraunhofer refractor after dinner, Galle read out the stars he saw and d'Arrest checked them against the chart. After a few minutes Galle called an eighth-magnitude object at right ascension 21h 53m 25.84s, declination –13°24'. d'Arrest exclaimed, "This star is not on the map!" It was fifty-five arcminutes — less than one degree — from Le Verrier's predicted position. They confirmed the object's motion against the fixed stars the next night, then sent word to Le Verrier. The eighth planet had been discovered by mathematics before it had been seen. Adams's papers were retrieved from Airy's files; both men were formally credited, though in different ratios by the French and English communities for decades. The planet was named Neptune, after considerable diplomatic wrangling, over Le Verrier's own preferred name (which was, characteristically, Le Verrier). Voyager 2 flew past Neptune on 25 August 1989. In every image it returned, the planet is a deep, still blue.