Discovery of Neptune

The planet Neptune is a planet which has been claimed to have been discovered through mathematics alone. Discussions on this topic revolve around a claim that the position of Neptune was predicted and discovered through Newton's Laws of Gravitation, and that it is therefore a confirmation of Newton's theory.

Writer and astronomer Jeffrey Bennett describes this assertion (Archive):

  “ Neptune's discovery was a triumph for the theory of gravity, developed by Isaac Newton in the late 1600s. By the mid-nineteenth century, careful observations of Uranus had shown its orbit to be slightly inconsistent with that predicted by Newton's theory of gravity. In the early 1840s, Englishman John Couch Adams suggested that the inconsistency could be explained by a previously unseen "eighth planet" orbiting the Sun beyond Uranus. By making calculations based on Newton's theory, he even predicted the location of the planet and urged a telescopic search. Unfortunately, Adams was a student at the time and was unable to convince British astronomers to carry out the search.

In the summer of 1846, French astronomer Urbain Leverrier made similar calculations independently. He sent a letter to Johann Galle, of the Berlin Observatory, suggesting a search for the eighth planet. On the night of September 23, 1846, Galle pointed his telescope to the position suggested by Leverrier. There, within 1° of its predicted position, he saw the planet Neptune. Hence, Neptune's discovery truly was made by mathematics and physics and was merely confirmed with a telescope. ”

Perturbation Theory

According to some sources we find that Neptune was actually discovered, in full or in part, on the basis of Perturbation Theory. Perturbation Theory predictions do not use the full laws of Newton, but are based on patterns. See: Astronomical Prediction Based on Patterns.

https://www.encyclopediaofmath.org/index.php/Perturbation_theory (Archive)

  “ The discovery of the planet Neptune in 1848 by J. Adams and U. le Verrier, based on the deviations in motion of the planet Uranus, represented a triumph of perturbation theory. ”

From Perturbation Theory in Celestial Mechanics (Archive) by Dr. Alessandra Celletti we read:

  “ Celestial Mechanics greatly motivated the advances of perturbation theories as witnessed by the discovery of Neptune: its position was theoretically predicted by John Adams and by Jean Urbain Leverrier on the basis of perturbative computations; following the suggestion provided by the theoretical investigations, Neptune was finally discovered on 23 September 1846 by the astronomer Johann Gottfried Galle. ”

Pre-Discovery Observations

Curiously, according to a depiction of its discovery it is described that Neptune was "pre-discovered" and that these observations were "important in accurately determining the orbit of Neptune."

https://en.wikipedia.org/wiki/Discovery_of_Neptune (Archive)

Neptune is too dim to be visible to the naked eye: its apparent magnitude is never brighter than 7.7.[5] 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.[6] 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.[7]

Discovered By Luck

https://earthsky.org/human-world/today-in-science-discovery-of-neptune (Archive)

  “ Ironically, as it turns out, both Le Verrier and Adams had been very lucky. Their predictions indicated Neptune’s distance correctly around 1840-1850. Had they made their calculations at another time, both predicted positions would have been off. Their calculations would have predicted the planet’s position only 165 years later or earlier, since Neptune takes 165 years to orbit once around the sun.

By the way, Neptune might have been discovered without the aid of mathematics. Like all planets in our solar system – because it’s closer to us than the stars – it can be seen from Earth to move apart from the star background. For example, the great astronomer Galileo, using one of the first telescopes, is said to have recorded Neptune as a faint star in 1612. If it had watched it over several weeks, he’d have noticed its unusual motion. ”

http://www.helas.gr/conf/2011/posters/S_5/dallas.pdf (Archive)

  “ Airy seems to be the only scientist involved in the discovery that has thoughts of a possible modification of Newtonian gravity to explain the irregular movement of Uranus. But nowhere in his memoire is there a statement that the discovery of Neptune is a test, let alone a critical one, of the law of gravitation. It was apparent shortly after the discovery that luck played its part in the easy discovery of Neptune. The whole process is extremely error prone, in both the calculations and the observations, so if the planet were not discovered in the circumstances of 1846, this would not be a refutation of Newtonian gravity, but simply a refutation of the auxiliary prepositions. ”

American Journal of Science and Arts

From Vol IV of the American Journal of Science and Arts, November, 1847, we read the following from astronomer Sears C. Walker:

  “ If we admit for the moment that my views are correct, then LeVerrier's announcement of March 29th is in perfect accordance with that of Professor Peirce of the 16th of the same month, viz. that the present visible planet Neptune is not the mathematical planet to which theory had directed the telescope. None of its elements conform to the theoretical limits. Nor does it perform the functions on which alone its existence was predicted, viz. those of removing that opprobrium of astronomers, the unexplained perturbations of Uranus.

We have it on the authority of Professor Peirce that if we ascribe to Neptune a mass of three-fourths of the amount predicted by LeVerrier, it will have the best possible effect in reducing the residual perturbations of Uranus below their former value; but will nevertheless leave them on the average two-thirds as great as before.

It is indeed remarkable that the two distinguished European astronomers, LeVerrier and Adams, should, by a wrong hypothesis, have been led to a right conclusion respecting the actual position of a planet in the heavens. It required for their success a compensation of errors. The unforeseen error of sixty years in their assumed period was compensated by the other unforeseen error of their assumed office of the planet. If both of them had committed only one theoretical error, (not then, but now believed to be such,) they would, according to Prof. Peirce's computations, have agreed in pointing the telescope in the wrong direction, and Neptune might have been unknown for years to come. ”

Further References

The Planet Neptune in Earth Not a Globe