How Was Neptune Discovered? the Story of Mathematical Competition and an Unresolved Controversy

Updated on October 5, 2018
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Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Something is Wrong With Planet Uranus

When Uranus was discovered, it was a major accomplishment for the scientific community. Never before has a planet been discovered by anyone, for all the planets up to that point could be seen without any telescopic aid. Once found, Uranus was studied heavily. Astronomer Alexis Bouvard even compiled tables of various positions of Uranus in its orbit in order to extrapolate its orbit. People began to notice that when Kepler’s planetary laws (three rules that all orbiting bodies follow) were applied to Uranus, it had discrepancies that were not within observational error such as gravitational perturbations from the other solar system objects. In 1821, Bouvard commented in his book Tables for Uranus that, “… The difficulty of harmonizing the two systems is really due to the inaccuracy of early observations or whether it is due to some strange and at present unknown force acting upon the planet and influencing its movement” (Airy 123, Moreux 153). Many ideas came about to explain this, including the notion that gravity may work differently in that region of space (Lyttleton 216). In 1829, a scientist named Harrison supposed that not one but two planets must be affecting Uranus’ orbit (Moreux 153) However, the general consensus was that a single missing planet must exist past Uranus and pull on it with its gravity (Lyttleton 216).

What Were the Unknowns?

When searching for a new planet, there are many quantities to solve for. You will need to find the planets mass (mn) and its average distance from the sun (dn) which would involve knowing its semi-major axis and semi-minor axis (since all planetary bodies orbit in some form of an ellipse). This would give us its eccentricity (en). We also do not know if the planet orbits our plane but since all the planets orbit within +-4 degrees of the ecliptic, it is a safe assumption that an unknown planet will also (Lyttleton 218).

Initial Wanderings

George Airy, who was the Astronomical Royal of Britain and a central figure to this story, was first brought into this search by the Reverend T.J. Hussey in a letter from November 17, 1834. He mentions in his letter how he has heard of a possible planet beyond Uranus and looked for it using a reflector telescope, but to no avail. He presented the idea of using mathematics as a tool in the search but admitted to Airy that he would not be of much help in that regard. On Novemeber 23rd Airy writes back to the reverend and admits he too has been preoccupied with a possible planet. He had observed that Uranus' orbit deviated the most in 1750 and 1834, when it would be at the same point. This was strong evidence for an object pulling on the planet, but Airy felt that until more observations were made no mathematical tools would be of help (Airy 124).

The return of Halley's comet in 1835 also sparked interest in the search for the eight planet. After 76 years, scientists had the orbit figured and and awaited to see it.

The problem was, it came a day late.

Calculations were quickly made and based off the deviation, it pointed to a trans-Uranus object at 38 AU. With so many heavenly bodies not working as they were predicted to, the Royal Academy of Sciences in 1842 offered a cash prize to anyone who could find the missing planet (Weintraub 111).

John Couch Adams
John Couch Adams | Source

John Couch Adams and His Method

Adams, a British astronomer, was an undergraduate student when he began his search for the missing planet in 1841. He had compiled himself additional observational errors in Uranus’ orbit. Starting in 1843, he began his calculations for the unknowns mentioned before and by 1845 he finally finished (Lyttleton 219).

Among the tools he used to solve for Neptune’s orbit was a false correlation known as Bode’s Law which noted that the distance from Saturn to the Sun was twice the distance from Jupiter to the Sun and that the distance from Uranus to the Sun was twice the distance from Saturn to the Sun, and so on. Essentially, it states that the distance from a planet to the Sun is twice the distance from the previous planet to the Sun. As it turns out, Bode’s Law fails to correctly place Mercury and it requires a planet to be placed between Mars and Jupiter if the pattern is to hold. Bode’s Law will ultimately fail on Neptune also (217).

Along with using Bode’s Law, Adams also used a circular orbit as his initial attempt to a solution. He knew that it would not be correct but it was a good starting point to compare it with the observational data and refine it to a more elliptical orbit as he iterated more solutions (Moreux 158).

As he worked in these calculations Adams needed data from past observations and he contacted Challis, who was in charge of the observatory at Cambridge. In a letter dated February 13, 1844 Challis writes to Airy. He requested the errors in the "geocentric longitudes" and "heliocentric longitudes" of Uranus, from 1818 to 1826. Airy does even better and sends data from 1754 to 1830 as well as notes on any discrepancies there may be from other published material that existed at the time (Airy 129).

George Biddel Airy
George Biddel Airy | Source

Airy and His Mistake

In a letter dated September 22, 1845 Challis writes to Airy about Adams' finished work and his desire to meet with Challis and Airy to discuss them. Airy responds September 29th that such a meeting would be a great idea and that Adams should write to Airy to settle the date (Airy 129).

On October 21, 1845, Adams sends his work to Airy in hopes that he would assist him in the search for Neptune. Adams did not seem to have enough conviction in his work to officially submit it for publication and would eventually revise his work several times. Adams was foremost a mathematician and an astronomer second. He may have wanted his work in more capable hands before taking the plunge of making his work official. (Rawlins 116).

Officially, Airy does not fully appreciate what he has received. He feels that certain portions of Adams work are assumed numbers when in reality Adams had made hard calculations over those elements. Airy was also more focused on how Adams work could help solve a problem with the radius vector of Uranus, or the distance problem that helped spark the quest for a new planet in the first place, than with the implications of Adam’s work. He writes back to Adams on November 5th expressing this (Lyttleton 221-2, Airy 130).

Finally, he also mentions in his letter to Adams that he has concerns about if the data takes into account recently measured errors in the orbits of Jupiter and Saturn because of gravitational tugging between them all. Naturally, not having his request met and instead being dealt all these comments and questions made Adams mad. He does not respond to Airy (222-3).

Urbain Le Verrier
Urbain Le Verrier | Source

Enter Le Verrier

Around this same time, an astronomer named Arago, director of the Paris Observatory, encourages a young French astronomer name Urbian Le Verrier to go find this missing planet (Moreux 153). Unaware of Adams and his work, Le Verrier did use some similar techniques as Adams. He too felt that Bode’s Law was an acceptable tool to find the distance to Neptune from the Sun. He also made similar conclusions about the plane of the orbit as well as the maximum number of degrees it could be above/below the ecliptic (155).

Le Verrier did many different calculations from Adams. He started by tracing out Uranus’ 84 year orbit and taking into account all known influences including gravitational pulls from Saturn and Jupiter. To help determine this orbit, Le Verrier needed to know the elements of an elliptical orbit that would best match. He also needed to know what his uncertainty values were for each of those values calculated (Lyttleton 231). Also using this model, original measurements of Uranus and current (at the time) measurements of Uranus, he made a calculation for the mass of Neptune which he felt would be smaller than Uranus (Moreux 154).

To get a feel as to how grueling the calculations both men worked on were, consider the following: During one portion of his work, Le Verrier was presented with 40 possible solutions to a particular value, based on unknowns such as satellites of Uranus, the range of Uranus' orbit, different space physics, or alterations to gravity. He solved for each value, and then determined which one was the best fit to his data (Lyttleton 232, Levenson 36-7). Also consider this: The Theory of the Perbutations, which contains some of Le Verrier and Adams calculations, has said values for Jupiter, Saturn, Uranus, and Neptune properties. This encompasses 5 volumes and totals about 2,300 pages. The actual calculations behind the values in the book take up about 3-4 times as much space (Moreux 156).

Chart showing Adam's and Le Verrier's predicitons and the actual location upon discovery. Note that this chart was done days before Neptune completed its first observed orbit, which takes 165 years.
Chart showing Adam's and Le Verrier's predicitons and the actual location upon discovery. Note that this chart was done days before Neptune completed its first observed orbit, which takes 165 years. | Source

The Hunt Is On, The Conspiracy Plotted

Le Verrier publishes his first set of calculations on November 10, 1845 and later his second set on June 1, 1846. Interestingly between these publications Airy reads of Le Verrier's work in December 1845 and remarks on his ability to incorporate Jupiter and Saturn's perturbations on Uranus, thus reducing errors in his work. With Adam's work in tow, he notes the similarities with Le Verrier's and is further persuaded by the mounting evidence that surrounds him. Yet amazingly, Airy is still concerned about the radius vector problem and does not appreciate the real meaning behind the work. Without revealing Adam's work, Airy writes to Le Verrier on June 26, 1846 about the Uranus radius vector problem that still plagued him. Le Verrier writes back, explaining how his work solves that problem. Airy does not write back (Lyttleton 224, Airy 131-2)

It took him 11 months to complete his final calculations but on August 31, 1846, Le Verrier makes his prediction before the Académie in France: Neptune would be at 326 degrees, 32’ on January 1, 1847 (155). The next day, September 1, 1846, Le Verrier publishes his findings in Comptes Rendus, a French scientific periodical. By this point, it had been 7 months since Airy had received Adams work (Lyttleton 224, Levenson 38).

As it turns out, Airy had a secret search for Neptune started with Challis' assistance. Since the expected location of Neptune was in a region the observatory had not cataloged before, Challis was not too hopeful with the odds of success. Why? One needs to find out what are stars, comets, asteroids, and so on before one can determine a planet so that the proper distinction can be made and you don't falsely claim that a planet has been found (Lyttleton 225).

In a shocking twist of events, Airy began this hunt without revealing to either Adams or Le Verrier that he was using their work. He read Le Verrier’s work abound the 24th of June, months before its final publication courtesy of a friend of Le Verrier, and held a meeting of the Board of Visitors of the Royal Observatory at Cambridge on June 29th where he points out many of the similarities of Adams and Le Verrier’s work. It was because of this similarity that he initiated the search, not because of the possible veracity of Adam’s initial submission. Airy mentions how if the task was distributed amongst observatories then the likelihood of discovery would increase. General agreement was reached on the matter but no game plan was set forth to move onward (Rawlins 117-8, Airy 133).

A few weeks later on July 9th Airy writes to Challis asking for his assistance in the search. Challis had been present at the meeting and so knew of the agreement in the work of Adams and Le Verrier. As Challis admitted in a letter, “I can say, however, that this concurrent evidence of the reality of the disturbing body from two independent investigations, weighed strongly with me in coming to the determination of undertaking the observations in the face of the great amount of labor they might be expected to entail.” Whether Airy was truly concerned about the radius vector problem is certainly doubtful and was most likely a cover for him to be clandestine in his operations (Rawlins 121, Airy 133).

Airy was determined to be the one to find the new planet. He was so desperate to use the telescope at Cambridge that he was willing to pay Challis, who was not on board at first, a large sum of money. He was able to subtlety mention this payment in the July 9th letter, saying it would be for an assistant if needed be. He further states that Challis' Northumberland Telescope was perfect because Airy's location was bad based on where the sky needed to be observed. No doubt that Airy was making a conspiracy, for many of his letters reveal his secrecy. For a good example look no further than a letter to Challis on November 13, 1846 (post-Neptune discovery): “The matter being one of delicacy, I will not compromise any one…All I as is will you allow me to publish your correspondence with me on this subject, or extracts from it taken at my discretion?” In fact once Neptune was found Airy destroyed many correspondences he had at the time. Several letters were sent between June 30th to July 21st and finally on July 27,th months before Le Verrier would publish his finalwork, their secret mission began (Rawlins 118-20, Airy 135, 142).

It is no surprise that Challis missed finding Neptune. Adam’s solution included a span of the night sky that covered longitudes between 315 and 336 degrees. That is so much to look over. Also, Adams sent so many revisions to his work that portions of the search became redundant (Rawlins 120).

Rather than wait around for what he thought was further inaction, Adams kept busy. Though he certainly could have initiated the search himself, much less publish his calculations, he was busy revising his work as was Le Verrier. Adams claimed on September 2, 1846, in a letter to Airy just a few days after Le Verrier published his latest work on the calculations, that he had not initiated the search yet because he did not want to hunt for something that was not more determined to be correct. Le Verrier would go on to publish a revised solution. Adams would not. Le Verrier’s new work reflects recent data from Uranus and other celestial objects while Adams’s was more about tinkering about based on an idea rather than on observations. One of these was modifying Bode's Law so that the distance was decreased by 1/30 and thus the eccentricity errors were reduced. All of this is further evidence to his lack of faith in his work (Rawlins 116-7, Airy 137).

On September 18, 1846, Le Verrier writes a letter to Dr. Galle, the director of the Berlin Observatory, about many topics and as a post-script mentions his calculations for Neptune (Moreux 156, Levenson 39). On September 23rd, Galle receives Le Verrier’s letter. The Berlin Observatory had recently compiled a map of the supposed region where Neptune would be located, so they would be able to tell what was a celestial object was and what was a planet (Lyttleton 225). The same day he received the letter, Galle and his assistant d’Arrest begin the search at night. Within the 1st hour of the search, a "star that is not on the map" as d'Arrest proclaimed was found a mere 52’ from its anticipated location (Moreux 157, Levenson 39). They took an extra night to confirm their discovery and formally announced it to the world on September 25th (Lyttleton 226).

When news reached Britain, Challis stopped his search. It was not noted until reviewing their work that Challis had observed Neptune several times during his hunt and had never realized it. In a letter from October 12th Challis tells Airy that he had an unnoticed find of the planet in early August. He continues on, saying how on August 12th he has noticed an 8th magnitude star that did not match with his July 31th observation of the same part of the sky. He had been busy completing a catalogue of comet observations and did not have the time to look over old results yet. He was too busy gathering data. The additional insult to injury was the examination of the area on September 29th after Le Verrier had published a new set of results. Challis thought that he say a disc but was not sure. Altogether, Neptune had been observed twice in the first four days on the search and many more times throughout (Airy 143, Lyttleton 225).

Le Verrier
Average Distance from Sun (AU)
Mass (10^24 kg)
Location (Degrees)


For England, the message was quite clear: They missed out on a great, once-in-a-lifetime discovery. They had knowledge of this planet a full year before it was found and now no credit would go to Adams, Airy, or Challis. Adams can hardly shoulder all the blame, for Challis had clearly missed the signs of Neptune and Airy has several offenses we can credit him with. Airy had the information at hand and tried to outmaneuver both men, only to come up empty-handed. In an attempt to perhaps save his own skin, he publicly gives Le Verrier credit for the find, earning the scorn of Britains for the rest of his life. Despite this, Airy did manage to prevent Le Verrier from winning the Royal Astronomical Society Medal for his work, which would have meant that Adams work was not on par with Le Verrier. Adams became an inspiration for several generations of British mathematicians. Not at any point in his work did he learn of Le Verrier’s prior to the discovery. Adams would acknowledge his mistake of not being bold with his work. In a letter from December 17, 1846, Adams wrote, “I fully allow that I have to blame myself severely in this matter…for having trusted to anyone but myself to make known the results at which I had arrived.” For Le Verrier, it ensured his place in French mathematical astronomy, a pedestal shared with Lagrange and Laplace (Lyttleton 226, Rawlins 117-8).

The world was excited by the find, for never before had mathematics predicted a natural object. This confidence in the results was lessened, however, when discrepancies were noticed in the calculated values and the actual ones (Lyttleton 227). For example, Adams calculated an orbital period of 227 years and Le Verrier found it to be 218 years using Kepler’s Third Law (Period squared is proportional to average distance cubed). The actual value of the orbit is 165 years. This discrepancy was not a result of using Kepler’s Third Law but because of using Bode’s Law for the average distance (229).

The only actual value they were close to, if one looks at the table, is the location in the sky it would be found. It is possible that both men were simply lucky with this. We shall never truly know (233). Neptune, the last planet in our Solar System, proved to be the ultimate challenge in mathematical astronomy.

Works Cited

Airy, Georges. Royal Astronomical Society Vol. 7 No. 9: 13 Nov. 1846. Print. 16 Nov. 2014.

Levenson, Thomas. The Hunt for Vulcan. Pandin House: New York, 2015. Print. 36-9.

Lyttleton, Raymond Arthur. Mysteries of the Solar System. Oxford: Clarendon P., 1968. 216-33. Print.

Moreux, Théophile. "Uranus & Neptune." Astronomy To-day. Trans. C. F. Russell. New York: E.P. Dutton and, 1926. 153-58. Print.

Rawlins, Dennis. "The Neptune Conspiracy." DIO 2.3 (1992): 116-21. Print.

Weintraub, David A. Is Pluto a Planet? New Jersey: Princeton University Press, 2007: 111. Print.

Questions & Answers

    © 2013 Leonard Kelley


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      • 1701TheOriginal profile imageAUTHOR

        Leonard Kelley 

        5 years ago

        Thanks Alun, it sure is tricky to express many of these ideas without the underlining math, and yet they need be summarized in an easily digestible fashion. Stay tuned, for I will be having an update to this hub that shows that Airy may have been more involved than we had suspected...

      • Greensleeves Hubs profile image

        Greensleeves Hubs 

        5 years ago from Essex, UK

        It is always fascinating to unravel how great scientific discoveries are made, and this is no exception. It's particularly revealing how often it happens that lucky breaks and mistakes influence the final discovery. Here it was clearly the case that had certain scientists - notably George Airy - perceived the significance of the evidence presented to them, then the discovery of Neptune might have been achieved earlier and attributed to different astronomers.

        Thanks for presenting this article. It is difficult to explain the details of mathematical calculations necessary for a study such as this, but I think you have made the search for Neptune and the problems encountered, accessible to all.

        Voted up. Alun


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