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.
“ 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. ”
According to various sources we find that Neptune was discovered on the basis of Perturbation Theory.
“ 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. ”
“ 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. ”
“ Le Verrier began by re-evaluating, to the 7th order, the technique of calculating the planetary perturbations known as the perturbing function. ”
See Astronomical Prediction Based on Patterns for information on Perturbation Theory.
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."
“ Neptune is too dim to be visible to the naked eye: 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. ”
Discovered By Luck
Other sources tell us that the planet was discovered by luck, rather than the reliability of any mathematical model.
“ 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. ”
“ 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. ”
“ Le Verrier sent his calculations to German astronomer Johann Gottfried Galle in Berlin, and sure enough, when Galle looked for a planet at the position Le Verrier’s calculations indicated they should look, he found Neptune.
Although later discovered to be primarily good luck, this was still a stunning achievement; a career-defining success for Le Verrier. Like anyone else would have, he wanted to repeat it. ”
From an essay Leverrier: The Zenith and Nadir of Newtonian Mechanics (Archive) by philosopher of science Norwood Russell Hanson (bio):
“ Furthermore, the actual orbit plotted for Neptune by Adams is different from that plotted by Leverrier; indeed, both plots depart from the actual path of the planet, Adams’ rather more widely. Fortunately, Adams and Leverrier began to worry about Uranus just when its deviation from the predicted path had reached its maximum: it was beginning to decrease.1 For a short time, and through a small segment of arc, “The Leverrier orbit”, “the Adams orbit”, and Neptune’s actual orbit were in close proximity. At any other time and place in the sky all three would have diverged. ”
Science historian Nicholas Kollerstrom states that dishonesty was involved with this claim.
“ In an interview in 2003, historian Nicholas Kollerstrom concluded that Adams's claim to Neptune was far weaker than had been suggested, as he had vacillated repeatedly over the planet's exact location, with estimates ranging across 20 degrees of arc. Airy's role as the hidebound superior willfully ignoring the upstart young intellect was, according to Kollerstrom, largely constructed after the planet was found, in order to boost Adams's, and therefore Britain's, credit for the discovery. ”
American Journal of Science and Arts
“ 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. ”
Earth Not a Globe
THE PLANET NEPTUNE
“ FOR some years the advocates of the earth's rotundity, and of the Newtonian philosophy generally, were accustomed to refer, with an air of pride and triumph, to the supposed discovery of a new planet, to which the name of "Neptune" was given, as an undeniable evidence of the truth of their system or theory. The existence of this luminary was said to have been predicated from calculation only, and for a considerable period before it was seen by the telescope. The argument was, "That the system by which such a discovery was made, must, of necessity, be true." An article which appeared in the "Illustrated London Almanack," for 1847, contained the following words:
- "Whatever view we take of this noble discovery, it is most gratifying, whether at the addition of another planet to our list, whether at the proving the correctness of the theory of universal gravitation, or in what view soever, it must be considered as a splendid discovery, and the merit is chiefly due to theoretical astronomy. This discovery is perhaps the greatest triumph of astronomical science that has ever been recorded."
If such things as criticism, experience, and comparative observation did not exist, the tone of exultation in which the above-named writer indulges might still be shared in by the astronomical student; but let the following summary of facts and extracts be carefully read, and it will be seen that such a tone was premature and unwarranted.
- "In the year 1781, Uranus was discovered by Sir William Herschel. . . . Between 1781 and 1820, it was very frequently observed; and it was hoped that at the latter time sufficient data existed to construct accurate tables of its motions. . . . It was found utterly impossible to construct tables which would represent all the observations. . . . Consequently it was evident that the planet was under the influence of some unknown cause. Some persons talked of a resisting medium, others of a great satellite which might accompany Uranus; some even went so far as to suppose that the vast distance Uranus is from the sun caused the law of gravitation to lose some of its force; others thought of the existence of a planet beyond Uranus, whose disturbing force caused the anomalous motions of the planet; but no one did otherwise than follow the bent of his inclination, and did not support his assertion by any positive considerations. Thus was the theory of Uranus surrounded with difficulties, when M. Le Verrier, an eminent French mathematician, undertook to investigate the irregularities in its motions. . . . The result of these calculations was the discovery of a new planet in the place assigned to it by theory, whose mass, distance, position in the heavens, and orbit it describes round the sun, were all approximately determined before the planet had ever been seen, and all agrees with observations, so far as can at present be determined." 1
The first paper by M. Le Verrier appeared on the 10th of November, 1845, and a second on June 1st, 1846; and "on the 23rd of September, Dr. Galle, at Berlin, discovered a star of the eighth magnitude, which was proved to be the planet," so it was thought; and hence, had it been true, the Newtonian philosophers had good cause to be proud of the theory which had apparently led to such grand results; and, as in the other "great discovery" by the celebrated French mathematician, M. Foucault, of the earth's motion by the vibrations of a pendulum, the peals of triumph rung by mathematicians were for months ringing in the ears of the whole civilised community. The whole of this scientific rejoicing was, however, suddenly arrested by the appearance, two years afterwards, of a paper by M. Babinet, read before the French Academy of Sciences, in which great errors in the calculations of M. Le Verrier were disclosed, as will be seen by the following letter:--
- Paris, September 15, 1848.
- "The only sittings of the Academy of late in which there was anything worth recording, and even this was not of a practical character, were those of the 29th ult., and the 11th inst. On the former day M. Babinet made a communication respecting the planet Neptune, which has been generally called M. Le Verrier's planet, the discovery of it having, as it was said, been made by him from theoretical deductions which astonished and delighted the scientific public. What M. Le Verrier had inferred from the action on other planets of some body which ought to exist was verified--at least, so it was thought at the time--by actual vision. Neptune was actually seen by other astronomers, and the honour of the theorist obtained additional lustre. But it appears, from a communication of M. Babinet, that this is not the planet of M. Le Verrier. He had placed his planet at a distance from the sun equal to thirty-six times the limit of the terrestrial orbit. Neptune revolves at a distance equal to thirty times of these limits, which makes a difference of nearly two hundred millions of leagues! M. Le Verrier had assigned to his planet a body equal to thirty-eight times that of the earth; Neptune has only one-third of this volume! M. Le Verrier had stated the revolution of his planet round the sun to take place in two hundred and seventeen years; Neptune performs its revolutions in one hundred and sixty-six years! Thus, then, Neptune is not M. Le Verrier's planet, and all his theory as regards that planet falls to the ground! M. Le Verrier may find another planet, but it will not answer the calculations which he had made for Neptune.
- "In the sitting of the 14th, M. Le Verrier noticed the communication of M. Babinet, and to a great extent admitted his own error. He complained, indeed, that much of what he said was taken in too absolute a sense, but he evinces much more candour than might have been expected from a disappointed explorer. M. Le Verrier may console himself with the reflection that if he has not been so successful as he thought he had been, others might have been equally unsuccessful; and as he has still before him an immense field for the exercise of observation and calculation, we may hope that he will soon make some discovery which will remove the vexation of his present disappointment." 2
- "As the data of Le Verrier and Adams stand at present, there is a discrepancy between the predicted and the true distance, and in some other elements of the planet. . . . It 'would appear from the most recent observations, that the mass of Neptune, instead of being, as at first stated, one nine thousand three hundredth, is only one twenty-three thousandth that of the sun; whilst its periodic time is now given with a greater probability at 166 years, and its mean distance from the sun nearly thirty. Le Verrier gave the mean distance from the sun thirty-six times that of the earth, and the period of revolution 217 years." 3
Thus we have found that "a discovery which was incontestably one of the most signal triumphs ever attained by mathematical science, and which marked an era that must be for ever memorable in the history of physical investigation," and which "some years ago excited universal astonishment," 4 was really worse than no discovery at all; it was a great astronomical blunder. An error of six hundred millions of miles in the planet's distance, of two thirds in its bulk, and of fifty-one years in its periodic time, ought at least to make the advocates of the Newtonian theory less positive, less fanatical and idolatrous--for many of them are as greatly so as the followers of Juggernauth--and more ready to acknowledge what they ought never to forget--that, at best, their system is but hypothetical, and must sooner or later give place to a practical philosophy, the premises of which are demonstrable, and which is, in all its details, sequent and consistent. Will they never learn to value the important truth, that a clear practical recognition of one single fact in nature is worth all the gew-gaw hypotheses which the unbridled fancies of wonder-loving philosophers have ever been able to fabricate? ”
- 1 "Illustrated London Almanack" for 1847.
- 2 "Times" Newspaper of Monday, September 18, 1848.
- 3 "Cosmos," by Humboldt, p. 75.
- 4 "How to Observe the Heavens," by Dr. Lardner, p. 173.
The Planet Vulcan
Le Verrier later went on to "discover" the planet Vulcan with his same methods:
“ One of the most interesting stories in astronomy concerns the history of what was once believed to be an intra-mercurial planet—Vulcan. The story begins in 1859 when the planet was “discovered’ by Urbain Jean Joseph Leverrier.
Leverrier was born on March 11, 1811, the son of a French civil servant. His birthplace, Saint Lo, is now familiar to most of us as the place where the allies “broke out” after the Normandy landings in the last world war.
Jean Leverrier introduced a new concept into planetary discovery. As he was a mathematical, rather than an observational astronomer, there is some basis for the belief that he never looked through a telescope. He discovered planets while seated at his desk in the Ecole Polytechnique in Paris. His first discovery was Neptune; his second was Vulcan. ”