Discovery of Neptune - Irregularities in Uranus's Orbit

Irregularities in Uranus's Orbit

In 1781, Anders Johan Lexell was the first to compute the orbit of Uranus and notice that it had irregularities. He suggested that there might be other planets in the Solar System that perturb the orbit of Uranus, with the Solar system ranging as far as 100 A. U.

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 or "residuals", both in the planet's ecliptic longitude and in its distance from the Sun, or radius vector, might be explained by a number of 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 as-yet undiscovered eighth planet.

Adams learned of the irregularities while still an undergraduate and became convinced of the "perturbation" hypothesis. Adams believed, in the face of anything that had been attempted before, that he could use the observed data on Uranus, and utilising nothing more than Newton's law of gravitation, 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 calculating the first of six iterations.

In modern terms, the problem is an inverse problem, an attempt to deduce the parameters of a mathematical model from observed data. Though the problem is a simple one for modern mathematics after the advent of electronic computers, at the time it involved much laborious hand calculation. Adams began by assuming a nominal position for the hypothesised body, using the empirical Bode's law. He then calculated the path of Uranus using the assumed position of the perturbing body and calculated the difference between his calculated path and the observations, in modern terms the residuals. He then adjusted the characteristics of the perturbing body in a way suggested by the residuals and repeated the process, a process similar to regression analysis.

On 13 February 1844, James Challis, director of the Cambridge Observatory, requested data on the position of Uranus, for Adams, from Astronomer Royal George Biddell Airy at the Royal Observatory, Greenwich. Adams certainly completed some calculations on 18 September 1845.

Supposedly, Adams 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 Sampson suggested a note in Adams's papers that describes "the New Planet" and is endorsed, in handwriting 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 only after the fact by someone other than Adams. Further, 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, remarking "while the labour was certain, success appeared to be so uncertain."

Meanwhile, Urbain Le Verrier, on November 10, 1845, presented to the Académie des sciences in Paris a memoir on Uranus, showing that the pre-existing theory failed to account for its motion. Unaware of Adams's work, he attempted a similar investigation, and on June 1, 1846, in a second memoir presented to a public meeting of the Académie, gave the position, but not the mass or orbit, of the proposed perturbing body. Le Verrier located Neptune within one degree of its predicted position.