The crowd of orbits disclosed by asteroidal detections invites attentive study. D'Arrest remarked in 1851,[1022] when only thirteen minor planets were known, that supposing their paths to be represented by solid hoops, not one of the thirteen could be lifted from its place without bringing the others with it. The complexity of interwoven tracks thus illustrated has grown almost in the numerical proportion of discovery. Yet no two actually intersect, because no two lie exactly in the same plane, so that the chances of collision are at present nil. There is only one case, indeed, in which it seems to be eventually possible. M. Lespiault has pointed out that the curves traversed by "Fidés" and "Maïa" approach so closely that a time may arrive when the bodies in question will either coalesce or unite to form a binary system.[1023]
The maze threaded by the 500 asteroids contrasts singularly with the harmoniously ordered and rhythmically separated orbits of the larger planets. Yet the seeming confusion is not without a plan.
The established rules of our system are far from being totally disregarded by its minor members. The orbit of Pallas, with its inclination of 34° 42′, touches the limit of departure from the ecliptic level; the average obliquity of the asteroidal paths is somewhat less than that of the sun's equator;[1024] their mean eccentricity is below that of the curve traced out by Mercury, and all without exception are pursued in the planetary direction—from west to east.
The zone in which these small bodies travel is about three times as wide as the interval separating the earth from the sun. It extends perilously near to Jupiter, and dovetails into the sphere of Mars.
Their distribution is very unequal. They are most densely congregated about the place where a single planet ought, by Bode's Law, to revolve; it may indeed be said that only stragglers from the main body are found more than fifty million miles within or without a mean distance from the sun 2·8 times that of the earth. Significant gaps, too, occur where some force prohibitive of their presence would seem to be at work. The probable nature of that force was suggested by the late Professor Kirkwood, first in 1866, when the number of known asteroids was only eighty-eight, and again with more confidence in 1876, from the study of a list then run up to 172.[1025] It appears that these bare spaces are found just where a revolving body would have a period connected by a simple relation with that of Jupiter. It would perform two or three circuits to his one, five to his two, nine to his five, and so on. Kirkwood's inference was that the gaps in question were cleared of asteroids by the attractive influence of Jupiter. For disturbances recurring time after time—owing to commensurability of periods—nearly at the same part of the orbit, would have accumulated until the shape of that orbit was notably changed. The body thus displaced would have come in contact with other cosmical particles of the same family with itself—then, it may be assumed, more evenly scattered than now—would have coalesced with them, and permanently left its original track. In this way the regions of maximum perturbation would gradually have become denuded of their occupants.
We can scarcely doubt that this law of commensurability has largely influenced the present distribution of the asteroids. But its effects must have been produced while they were still in an unformed, perhaps a nebular condition. In a system giving room for considerable modification through disturbance, the recurrence of conjunctions with a dominating mass at the same orbital point need not involve instability.[1026] On the whole, the correspondence of facts with Kirkwood's hypothesis has not been impaired by their more copious collection.[1027] Some chasms of secondary importance have indeed been bridged; but the principal stand out more conspicuously through the denser scattering of orbits near their margins. Nor is it doubtful that the influence of Jupiter in some way produced them. M. de Freycinet's study of the problem they present[1028] has, however, led him to the conclusion that they existed ab origine, thus testifying rather to the preventive than to the perturbing power of the giant planet.
The existence, too, of numerous asteroidal pairs travelling in approximately coincident tracks, must date from a remote antiquity. They result, Professor Kirkwood[1029] believed, from the divellent action of Jupiter upon embryo pigmy planets, just as comets moving in pursuit of one another are a consequence of the sundering influence of the sun.
Leverrier fixed, in 1853,[1030] one-fourth of the earth's mass as the outside limit for the combined masses of all the bodies circulating between Mars and Jupiter; but it is far from probable that this maximum is at all nearly approached. M. Berberich[1031] held that the moon would more than outweigh the whole of them, a million of the lesser bodies shining like stars of the twelfth magnitude being needed, according to his judgment, to constitute her mass. And M. Niesten estimated that the whole of the 216 asteroids discovered up to August, 1880, amounted in volume to only 1/4000th of our globe,[1032] and we may safely add—since they are tolerably certain to be lighter, bulk for bulk, than the earth—that their proportionate mass is smaller still. A fairly concordant result was published in 1895 by Mr. B. M. Roszel.[1033] He found that the lunar globe probably contains forty times, the terrestrial globe 3,240 times the quantity of matter parcelled out among the first 311 minor planets. The actual size of a few of them may now be said to be known. Professor Pickering, from determinations of light-intensity, assigned to Vesta a diameter of 319 miles, to Pallas 167, to Juno 94, down to twelve and fourteen for the smaller members of the group.[1034] An albedo equal to that of Mars was assumed as the basis of the calculation. Moreover, Professor G. Müller[1035] of Potsdam examined photometrically the phases of seven among them, of which four—namely, Vesta, Iris, Massalia, and Amphitrite—were found to conform precisely to the behaviour of Mars as regards light-change from position, while Ceres, Pallas, and Irene varied after the manner of the moon and Mercury. The first group were hence inferred to resemble Mars in physical constitution, nature of atmosphere, and reflective capacity; the second to be moon-like bodies.
Finally, Professor Barnard, directly measuring with the Yerkes refractor the minute discs presented by the original quartette, obtained the following authentic data concerning them:[1036] Diameter of Ceres, 477 miles, albedo = 0·18; diameter of Pallas, 304 miles, albedo = 0·23; diameter of Vesta, 239 miles, albedo = 0·74; diameter of Juno, 120 miles, albedo = 0·45. Thus, the rank of premier asteroid proves to belong to Ceres, and to have been erroneously assigned to Vesta in consequence of its deceptive brilliancy. What kind of surface this indicates, it is hard to say. The dazzling whiteness of snow can hardly be attributed to bare rock; yet the dynamical theory of gases—as Dr. Johnstone Stoney pointed out in 1867[1037]—prohibits the supposition that bodies of insignificant gravitative power can possess aerial envelopes. Even our moon, it is calculated, could not permanently hold back the particles of oxygen, nitrogen, or water-gas from escaping into infinite space; still less, a globe one thousand times smaller. Vogel's suspicion of an air-line in the spectrum of Vesta[1038] has, accordingly, not been confirmed.