The greatest triumph of the celestial mechanics built on gravitation and inertia to the exclusion of any other forces took place in 1846 when Neptune was discovered in the place in the sky calculated by Adams and Leverrier independently of each other; they indicated the direction where the planet would be found with the exactness of one degree; they calculated its position by considering the unaccounted for perturbations of Uranus. The story of its discovery is an exciting chapter in the history of astronomy: how the poor student Adams stood in the antechambers of the Royal Astronomer Airy and was sent away by the valet because Sir Airy was at the table, and how he tried to convince the powerful astronomer of the existence of an eighth planet by sending in his calculations; and how the Frenchman Leverrier was much more fortunate by having performed very similar calculations and by having sent them to the observatory at Potsdam where the young astronomer Gale, the very first night at the very first look at the indicated direction found the new planet. The excited scientific community in Europe was soon plunged into the debate who of the two was the true discoverer, or better prognosticator, since Gale was the discoverer of the planet; the passions were divided by the national line, with the French and British rivalries inflamed, and the Royal Astronomer had to defend his behavior; there exists quite a literature on the subject. The French insisted on their priority and even named the new planet Leverrier, and it took some time before its new name Neptune prevailed. Till today the case is debated and the pride of Britannia, in any event deprived of priority, of the greatest discoveries, is still not completely healed.
The discovery was hailed by the British and the Frenchand by everyoneas the greatest triumph of the Newtonian theory of gravitation. Uranus showed certain irregularities in its motion unaccounted for by the gravitational pull of the known planets, and the existence and the position of a planet not yet seen was claimed by Adams and Leverrier alike. This was possibly the best prognostication in the annals of science. But was it really so precise and was it such a triumph for Newton as always asserted?
The so-called Bodes Law is the empirically established regularity, covered by a simple formula, in the mean distances of the planets from the sun. This regularity can be traced through the planetary system from Mercury to Uranus (the one vacant place, between the orbits of Mars and Jupiter, was filled in, when in the first night of the nineteenth century Ceres, the first of the many asteroids was discovered by Piazzi Smyth). Adams and Leverrier alike assumed that the planet which causes unaccounted perturbations in Uranus must be located at a distance dictated by Bodes Law. And since Saturn, the sixth planet, is smaller than Jupiter, the fifth, and Uranus, the seventh, is smaller than Saturn, it would be quite logical to expect a planet smaller than Uranus at a distance of 1,750,000,000 miles from its orbit. But next the calculations showed that the distance of the two planets when in conjunction is not 1,750,000,000 miles but only roughly 1,000,000,000; and with the gravitational attraction decreasing with the distance as the inverse square of the latter, the mass of the newly discovered planet was grossly overestimated: it was supposed to exert the influence from a much greater distance than one actually found. It was not enough to show the direction where the planet would be found; it was necessary, in order that the prediction should be true, that the planet would be at the distance predicted, and it was not with Adams, nor with Leverrier, both of whom committed the same error. Therefore, when the great controversy raged between the supporters of Adams and those of Leverrier, some voices were heard that neither of them was a true prognosticator and there was no point in the rivalry. To make a distance error of 75 percent was equal to a threefold overestimate of the mass of the planet. In order to produce the effects from its true distance Neptune needed to be three times as massive as it actually is. Bodes Law broke down with the discovery of Neptune. And though Neptune is a little more massive than Uranus, the discrepancy between what was expected and what was found in no manner can be regarded as a rigid confirmation of the Newtonian celestial mechanics with an exact formula of attraction between masses at changing distances. The story is not yet at its end, and we need to tell of the discovery of Pluto, the ninth planet, which should have explained what Neptune left unexplained, but failed to do so, either, and by a still larger margin.
Yet in 1846 the discovery of Neptune was acclaimed, and because of the
inertia of the human mind, is still acclaimed as the greatest proof of
the truth of Newtonian celestial laws of gravitational mechanics.