CHAPTER IV
THE OUTER PLANETS
BEYOND Mars lies the domain of the asteroids, a domain vast in extent, that, untenanted by any large planet, stretches out to Jupiter. Occupied solely by a host of little bodies agreeing only in lack of size, even this space seems too small to contain them, for recent research has shown some transgressing its bounds. One, Eros, discovered by De Witt, more than trenches on Mars’ territory, having an orbit smaller than that of the god of war, and may be considered perhaps the forerunner of more yet to be found between Mars and the Earth. On the other side, three recently detected by Max Wolf at Heidelberg have periods equal to that of Jupiter, and in their motions appear to exemplify an interesting case of celestial mechanics pointed out theoretically by Lagrange long before its corroboration in fact was so much as dreamt. Achilles, Patroclus, and Hector, as the triad are called, so move as always to keep their angular distance from Jupiter unaltered in their similar circuits of the Sun.
Orbits of the Outer Planets.
Before considering these bodies individually, we may well look upon them en bloc, inasmuch as one attribute of the asteroids concerns them generically rather than specifically, and is of great interest both from a mechanical and an historical point of view. For, in fact, it is what led to their discovery. Titius of Wittenburg, about the middle of the eighteenth century, noticed a curious relation between the distances from the Sun of the then known planets. It consisted in a sort of regular progression, but with one significant gap. Bode was so struck by the gap that he peopled it with a supposed planet, and so brought the relation into general regard in 1772. In consequence, it usually bears his name. It is this: if we take the geometrical series, 3, 6, 12, 24, 48, 96 and add 4 to each term, we shall represent to a fair degree of precision the distances of the several planets, beginning with Mercury at 4 and ending with Saturn at 100, which was the outermost planet then known. All the terms were represented except 24 + 4, or 28—a gap lying between Mars and Jupiter. When Uranus was discovered by Sir William Herschel in 1781 and was found to be travelling at what corresponded to the next outer term 192 + 4, or 196, the opinion became quite general that the series represented a real law and that 28 must be occupied by a planet. Von Zach actually calculated what he called its analogical elements, and finally got up in 1800 a company to look for it which he jocularly described as his celestial police. Considering that Bode’s law is not a law at all, but a curious coincidence, as Gauss early showed in its lack of precision and in its failure to mark the place of Mercury with any approach to accuracy, and as the discovery of Neptune amply bore out, it was perhaps just in fate that the honor of filling the gap did not fall to any of the “celestial police,” but to an Italian astronomer, Piazzi, at the time engaged on a new star chart. An illness of Piazzi caused it to be lost almost as soon as found. In this plight an appeal was made to the remarkable Gauss, just starting on his career. Gauss undertook the problem and devised formulæ by which its place was predicted and the planet itself recovered. It proved to fit admirably the gap. But it had hardly been recovered before another planet turned up equally filling the conditions. Ceres, the first, lay at 26.67 astronomical units from the Sun; Pallas, the second, at 27.72. Two claimants were one too many. But the inventive genius of Olbers came to the rescue. By a bold hypothesis he suggested that since two had appeared where only one was wanted, both must originally have formed parts of a single exploded planet. He predicted that others would be detected by watching the place where the explosion had occurred, to wit: where the orbits of Ceres and Pallas nearly intersected in the signs of the Virgin and the Whale.
For in the case of an explosion the various parts, unless perturbed, must all return in time to the scene of the catastrophe. By following his precept, two more were in fact detected in the next two years, Juno and Vesta. His hypothesis seemed to be confirmed. No new planets were discovered, and the old fulfilled fairly what was required of them. Lagrange on calculation gave it his mathematical assent.
Nevertheless, it was incorrect, as events eventually showed, though for forty years it slept in peace, no new asteroids being found. We now know that this was because the rest were all much smaller, and for such nobody looked. It was not till 1845 that Hencke, an ex-postmaster of Driessen in Prussia, after fifteen years of search detected another, Astræa, of the 11th magnitude. After this discoveries of them came on apace, until now more than six hundred are known, and their real number seems to be legion. But those discovered are smaller each year on the average, showing that the larger have already been found. Their orbits are such that they cannot possibly ever have all formed part of a pristine whole. The idea, not the body, was exploded. For they are now recognized as having always been much as they are to-day.