Daniel Kirkwood

“ A body, therefore, weighing two hundred pounds at the earth's surface would on the surface of the asteroid weigh less than five ounces. At the earth's surface a weight falls sixteen feet the first second, at the surface of Menippe it would fall about one-fourth of an inch. A person might leap from its surface to a height of several hundred feet, in which case he could not return in much less than an hour. "But of such speculations," Sir John Herschel remarks, "there is no end."
The number of these planetules between the orbits of Mars and Jupiter in all probability can never be known. ”

“ Again, if Mercury's orbit had its present eccentricity when the radius [Pg 40] of the solar spheroid was twenty-nine million miles, the planet at its nearest approach to the centre of its motion must have passed through the outer strata of the central body. In such case a lessening of the planet's mean distance would be a necessary consequence. We thus see that in the formation of the solar system the eccentricity of an asteroidal orbit could not increase beyond a moderate limit without the planet's return to the solar mass. ”

“ According to this formula the distances of the planets from Mercury's orbit form a geometrical series of which the ratio is two. In other words, if we reckon the distances of Venus, the earth, etc., from the orbit of Mercury, instead of from the sun, we find that—interpolating a term between Mars and Jupiter—the distance of any member of the system is very nearly half that of the next exterior. Baron De Zach, an enthusiastic astronomer, was greatly interested in Bode's empirical scheme, and undertook to determine the elements of the hypothetical planet. ”

“ It does not secure the stability of all periodic comets nor of the meteor streams revolving about the sun. In the early stages of the system's development the matter moving in unstable orbits may have been, and probably was, much more abundant than at present. But even now, are we justified in concluding that all known asteroids have stable orbits? For the major planets the secular variations of eccentricity have been calculated, but for the orbits between Mars and Jupiter these limits are unknown. ”

“ With an eccentricity of 0.252 (less than that of many asteroids) , the distance of Hilda's aphelion would be greater than that of Jupiter's perihelion. It seems possible, therefore, that certain [Pg 41] minor planets may have their orbits much changed by Jupiter's disturbing influence. [8]
Whoever looks at a table of asteroids arranged in their order of discovery will find only a perplexing mass of figures. Whether we regard their distances, their inclinations, or the forms of their orbits, the elements of the members are without any obvious connection. ”

“ The extreme rarity of the zone between Mars and Jupiter, regarded as a single ring, is thus accounted for in accordance with known dynamical laws.
3. The Limits of Perihelion Distance.
It is sufficiently obvious that whenever the perihelion distance of a planet or comet is less than the sun's radius, a collision must occur as the moving body approaches the focus of its path. The great comet of 1843 passed so near the sun as almost to graze its surface. With a perihelion distance but very slightly less, it would have been precipitated into the sun and incorporated with its mass. ”

“ Subsequent observations soon revealed its planetary character, its mean distance corresponding very nearly with the calculations of De Zach. The discoverer called it Ceres Ferdinandea, in honor of his sovereign, the King of Naples. In this, however, he was not followed by astronomers, and the planet is now known by the name of Ceres alone. The discovery of this body was hailed by astronomers with the liveliest gratification as completing the harmony of the system. ”

“ The diameter of the former is to that of the earth as one to six hundred and sixty-four; and since spheres are to each other as the cubes of their diameters, it would require two hundred and ninety millions of such asteroids to form a planet as large as our globe. In other words, if the earth be represented by a sphere one foot in diameter, the magnitude of Menippe on the same scale would be that of a sand particle whose diameter is one fifty-fifth of an inch. ”

“ In the Uranian system the widest interval between adjacent orbits is just within the orbit of the bright satellite, Titania.
[Pg 39]
The foregoing facts suggest the inquiry, What effect would be produced by a large planet on interior masses abandoned by a central spheroid? As the phenomena in all instances would be of the same nature, we will consider a single case,—that of Jupiter and the asteroids.
The powerful mass of the exterior body would produce great perturbations of the neighboring small planets abandoned at the solar equator. ”

“ Throughout the greater part of the interval between Mars and Jupiter an almost continuous succession of small planetary masses—not nebulous rings—appears to have been abandoned at the solar equator. The entire cluster, [Pg 53] distributed throughout a space whose outer radius exceeds the inner by more than two hundred millions of miles, could not have originated, as supposed by Laplace, in a single nebulous zone the different parts of which revolved with the same angular velocity. ”

“ Harding, like Laplace, deeming it appropriate to place Juno near Jupiter, selected the name for the third minor planet, which is accordingly known by this designation.
Juno is distinguished among the first asteroids by the great eccentricity of its orbit, amounting to more than 0.25. Its least and its greatest distances from the sun are therefore to each other very nearly in the ratio of three to five. The planet consequently receives nearly three times as much light and heat in perihelion as in aphelion. ”

“ These peculiarities, together with the fact that the mean distances of Ceres and Pallas were nearly the same, and that their orbits approached very near each other at the intersection of their planes, suggested the hypothesis that they are fragments of a single original planet, which, at a very remote epoch, was disrupted by some mysterious convulsion. This theory will be considered when we come to discuss the tabulated elements of the minor planets now known. ”

“ The average eccentricity of the two hundred and sixty-eight asteroids whose orbits have been calculated is 0.1569. As with the orbits of the old planets, the eccentricities vary within moderate limits, some increasing, others diminishing. The average, however, will probably remain very nearly the same. An inspection of the table shows that while but one orbit is less eccentric than the earth's, sixty-nine depart more from [Pg 49] the circular form than the orbit of Mercury. ”

“ When a cosmical body is surrounded by a ring of considerable breadth, and has also exterior satellites at such distances that a simple relation of commensurability would obtain between the periods of these satellites and those of certain particles of the ring, the disturbing influence of the former will produce gaps or intervals in the ring so disturbed. ”

“ It seems not improbable, however, that an indefinite number of very small bodies belonging to the zone remain to be found. The process of discovery is becoming more difficult as the known number increases. The astronomer, for instance, who may discover number two hundred and seventy-two must know the simultaneous positions of the two hundred and seventy-one previously detected before he can decide whether he has picked up a new planet or merely rediscovered an old one. The numbers discovered in the several months are as follows:
[Pg 25]
This obvious disparity is readily explained. ”

“ Thus, if the ratio of the less to the greater period is expressed by the fraction 1⁄2, where the difference between the numerator and the denominator is one, the commensurability is of the first order ”

“ The astronomer who would undertake the search for new asteroids must supply himself with star-charts extending some considerable distance on each side of the ecliptic, and containing all telescopic stars down to the thirteenth or fourteenth magnitude. ”

“ How long the watch, if unsuccessful, might have been continued is doubtful. The object of research, however, was fortunately brought to light before the members of the astronomical association had fairly commenced their labors. [1]
On the 1st of January, 1801, Professor Giuseppe Piazzi, of Palermo, noticed a star of the eighth magnitude, not indicated in Wollaston's catalogue. ”

“ But this would be equal to five thousand planets, each as large as Vesta, to seventy-two millions as large as Menippe, or to four thousand millions of five miles in diameter. In short, the existence of an indefinite number too small for detection by the most powerful glasses is by no means improbable. The more we study this wonderful section of the solar system, the more mystery seems to envelop its origin and constitution.
6. The Orbits of the Asteroids.
The form, magnitude, and position of a planet's orbit are determined by the following elements:
1. ”