The Discovery of the Planet Neptune and the Flat-Earth Movement

Austin Whitsitt on the Discovery of Neptune

Recently on a flat-earth channel, I heard Austin and a non-flat-earther discussing the 1846 discovery of the planet Neptune. The discovery of Neptune is rightly described as a triumph of Newtonian mechanics, but Austin disagreed. In 1781, William Herschel stumbled across the planet Uranus while using one of his telescopes. This was big news because no one had discovered a planet since ancient times. The five naked-eye planets—Mercury, Venus, Mars, Jupiter, and Saturn—appear as bright stars in the sky, but the planets beyond Saturn generally are too faint to be seen with the naked eye, so it is not surprising that they were not discovered before the invention of the telescope. Once Uranus was discovered, observations of its changing position in the sky quickly led to the calculation of Uranus’ orbit. Uranus’ distance from the sun is about twice that of Saturn. For a few decades, Uranus followed its computed orbit, but eventually, it was obvious that Uranus was not quite following its predicted orbit. The discrepancy was small but significant. What was the cause of the discrepancy?

The slight variations of the planets’ orbits due to these perturbations were well understood by the time Uranus was discovered.

We generally think that the planets follow simple orbits around the sun. This is largely true. However, none of the planets exactly follow simple orbits with the sun as the sole gravitating body responsible for their orbits. All the planets have mass, so the gravity of each planet exerts a gravitational force on all the other planets. But since the sun has far more mass than all the planets (the planets combined have only 0.2% the mass of the sun), the sun’s gravity is the dominant force determining planetary orbits. The mutual gravitation of the planets are slight variations on the simple sun-only orbits of the planets. We call these small tugs the planets produce on one another perturbations. The slight variations of the planets’ orbits due to these perturbations were well understood by the time Uranus was discovered. In a sense, this is a triumph of Newtonian mechanics. The perturbations of the known planets could not account for the discrepancy in Uranus’ orbit, so it seemed plausible that an unknown eighth planet beyond the orbit of Uranus was responsible for the unexplained discrepancy.

By the mid-1840s, two mathematicians, John Couch Adams in England and Jean Joseph Urbain Le Verrier in France, took up this problem. Adams finished his computation of the position of the hypothetical eighth planet first, but he was unable to get observational astronomers to test his prediction by looking for the planet at his predicted position. Le Verrier was more successful in his request for observational astronomers to test his prediction, and it took the staff of the Berlin Observatory less than an hour of looking to find Neptune close to the position he had predicted, as well as close to Adams’ predicted position.

The discovery of Neptune is hailed as a triumph of Newtonian mechanics, but Austin will have none of it. In the recent program, Austin referred to a statement by a Harvard professor that the discovery of Neptune “must be regarded as a happy accident,” using this as his source. I checked this source, expecting that it was a Harvard website or at least was recently written by someone from Harvard. It isn’t, and it wasn’t. I don’t know who wrote this article. Reading the article, I found that it quoted Harvard mathematician Benjamin Peirce from the first volume (1847) of Proceedings of the American Academy of Arts and Sciences (now called Daedalus) the year after Neptune was discovered. Hence, Austin’s source is a secondary source, not a primary source. There isn’t much context for the quote in this source, but a search for the Peirce quote yielded this excellent discussion of its context. Peirce’s quote apparently was more about other things rather than the science involved in the discovery of Neptune.

Furthermore, this article is a good discussion of the specifics of the predictions of Adams and Le Verrier. Austin mentioned the orbital size computed by Adams and Le Verrier being incorrect, which was the basis of Peirce’s characterization of the discovery of Neptune being “a happy accident.” It is clear from the way that Austin handled this that he does not understand the subject. For instance, in discussing Peirce’s statement that the discovery of Neptune was a happy accident, Austin’s source said, “I personally think that’s going a bit far.” Furthermore, Austin’s source characterized Le Verrier’s predicted position as being in “stunning proximity to the spot where Neptune was actually discovered.” Thus, Austin’s source gives a very different spin on the discovery of Neptune than what Austin claimed.

Why was the distance of Neptune from the sun in both Adams’ and Le Verrier’s calculations incorrect? It is one thing to calculate the perturbation of one planet on another planet knowing the mass and position of the perturbing planet. But the reverse problem, from the observed perturbation of a known planet calculating the mass and position of the unknown perturbing planet, is a much more difficult problem (this is called the n-body problem, which I shall discuss shortly). It requires the use of many terms of an infinite series expansion. This is relatively easy with computers today, but two centuries ago, all computations were done by hand. To aid in their computations, Adams and Le Verrier made an initial simplifying assumption of the hypothetical eighth planet, the planet’s distance from the sun. They chose nearly 40 astronomical units from the sun as that distance. An astronomical unit (AU) is the average distance between the earth and the sun (the actual size of Neptune’s orbit is 30.1 AU). Why did Adams and Le Verrier choose nearly 40 AU for the average distance of the hypothetical eighth planet from the sun? That was the predicted position of a planet beyond Uranus predicted by Bode’s law.

Bode’s Law

Though he did not originate it, in 1772, Johann Elert Bode popularized what is often called Bode’s law. Bode’s law is a numerical relationship that supposedly predicts the distances of the planets from the sun, a, expressed in AU. Bode’s law has the form

a = 0.4 + x,

where x = 0, 0.3, 0.6, 1.2, 2.4, 4.8, 9.6, 19.2, . . . . That is, x is a series starting with zero, followed by 0.3, with each successive term doubling the previous term. This is not a true mathematical series in that the first term is not related to the subsequent terms. Rather, the first term is arbitrarily added to a true mathematical sequence.

The table shows a comparison of the orbital sizes of the planets predicted by Bode’s law compared to the actual orbital sizes of the planets. Notice that the orbital sizes of the planets known in 1772 (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) closely match those predicted by Bode’s law. Also notice that Bode’s law predicted a planet between Mars and Jupiter, though no planet was known to be there. Bode’s law also predicted that if a planet existed beyond Saturn, it ought to be 19.6 AU from the sun. Bode’s law may not have been taken very seriously if not for the discovery of Uranus just a few years later, in 1781. The predicted orbital size nearly matched the orbital size of Uranus. A further boost came in 1801 with the discovery of Ceres, the first known asteroid, at 2.77 AU from the sun, which closely matched the prediction of Bode’s law of where a missing planet ought to be. Consequently, Ceres was considered a planet for more than 40 years. Bode’s law predicted an eighth planet would be 38.8 AU from the sun, but Neptune is 30.1 AU from the sun.

Since at the time of Adams’ and Le Verrier’s work Bode’s law was taken seriously, it was natural that they would ease the burden of computation by initially assuming that an eighth planet would have an orbital distance of 38.8 AU, as predicted by Bode’s law. Their computations reduced the average distance of the eighth planet slightly, to 37.26 AU in Adams’ model and 36.15 AU in Le Verrier’s model. With their hypothetical planet being farther from the sun than Neptune is, their computed mass for Neptune was greater than Neptune’s mass by 2–3 times. Neptune has a very circular orbit, but the assumption of the incorrect orbital size for Neptune required a relatively high eccentricity for the predicted orbit. Consequently, in the predicted orbits, Neptune was near perihelion, only 32 AU in Adams’ computation and 33 AU in Le Verrier’s computation. Note that this is within 10% of Neptune’s correct distance from the sun. Therefore, the situation was not nearly as bad as Austin claimed, based on Peirce’s gloomy assessment.

Once Neptune was spotted, observations of its changing position over just a few months allowed computation of its true orbit. It was clear that Adams’ and Le Verrier’s predicted orbits were wrong, but it was also clear that Neptune diverged from Bode’s law. This inevitably led to Bode’s law falling out of favor with astronomers. This loss of confidence in Bode’s law probably was related to the reclassification of Ceres as an asteroid rather than a planet. Since its discovery, Neptune has completed a little more than one orbit, and Neptune is observed to follow its computed orbit. That too is confirmation of Newtonian dynamics.

The n-Body Problem and Equivocation

Related to this discussion is the n-body problem, something that Austin has brought up many times and has gotten wrong. The computation of the orbits of two bodies under their mutual gravity is easily solved using Newton’s law of gravity. However, if a third (or more) body is introduced, then the problem of computing the orbits of the bodies in a simple form is not possible. This is the nature of computing the position of the hypothetical eighth planet. This problem is called the n-body problem, with n being an integer greater than two. As previously mentioned, the n-body problem is solved by using an infinite series of terms, with the higher-order terms converging toward zero. One can approximate an exact solution by carrying out computation to many terms until the remaining terms are not significant. This is very laborious when done by hand, but it is relatively easy using computers.

Austin often speaks of the n-body problem (sometimes calling it the three-body problem), obviously interpreting the word problem as a difficulty, trouble, or contradiction, thus disproving Newtonian mechanics. That is one definition of the word problem, but like many words, the word problem has more than one meaning. In mathematics or physics, the word problem refers to a proposition that is to be solved. Think of math problems, which are given to students to solve. Austin’s use of the word problem this way is an example of equivocation—substituting an inappropriate alternate meaning of a word. I’ve noticed that flat-earthers in particular often insist upon one and only one meaning for a word to the exclusion of all other meanings when it suits their purposes.

Conclusion

Time and time again I hear confident statements made by flat-earthers only to see that, despite their confidence, flat-earthers frequently do not properly understand the things that they claim. Austin Whitsitt’s recent discussion of Neptune’s discovery is yet another example. Unfortunately, many people mistake prominent flat-earthers’ confidence for correctness.

The discovery of Neptune was, indeed, a triumph of Newtonian physics and ultimately of operational science. The same operational science that disproves the flat earth.