Chapter III: The Asteroids

244. _Bode's Law of Planetary Distances._--There is a very remarkable law connecting the distances of the planets from the sun, which is generally known by the name of _Bode's Law_. Attention was drawn to it in 1778 by the astronomer Bode, but he was not really its author.

To express this law we write the following series of numbers:--

0, 3, 6, 12, 24, 48, 96;

each number, with the exception of the first, being double the one which precedes it. If we add 4 to each of these numbers, the series becomes--

4, 7, 10, 16, 28, 52, 100;

which series was known to Kepler. These numbers, with the exception of 28, are sensibly proportional to the distances of the principal planets from the sun, the actual distances being as follows:--

Mercury. Venus. Earth. Mars. ---- Jupiter. Saturn.

3·9 7·2 10 15·2 52·9 95·4

245. _The First Discovery of the Asteroids._--The great gap between Mars and Jupiter led astronomers, from the time of Kepler, to suspect the existence of an unknown planet in this region; but no such planet was discovered till the beginning of the present century. _Ceres_ was discovered Jan. 1, 1801, _Pallas_ in 1802, _Juno_ in 1804, and _Vesta_ in 1807. Then followed a long interval of thirty-eight years before _Astræa_, the fifth of these minor planets, was discovered in 1845.

246. _Olbers's Hypothesis._--After the discovery of Pallas, Olbers suggested his celebrated hypothesis, that the two bodies might be fragments of a single planet which had been shattered by some explosion. If such were the case, the orbits of all the fragments would at first intersect each other at the point where the explosion occurred. He therefore thought it likely that other fragments would be found, especially if a search were kept up near the intersection of the orbits of Ceres and Pallas.

Professor Newcomb makes the following observations concerning this
hypothesis:--

"The question whether these bodies could ever have formed a single
one has now become one of cosmogony rather than of astronomy. If a
planet were shattered, the orbit of each fragment would at first
pass through the point at which the explosion occurred, however
widely they might be separated through the rest of their course;
but, owing to the secular changes produced by the attractions of the
other planets, this coincidence would not continue. The orbits would
slowly move away, and after the lapse of a few thousand years no
trace of a common intersection would be seen. It is therefore
curious that Olbers and his contemporaries should have expected to
find such a region of intersection, as it implied that the explosion
had occurred within a few thousand years. The fact that the required
conditions were not fulfilled was no argument against the
hypothesis, because the explosion might have occurred millions of
years ago; and in the mean time the perihelion and node of each
orbit would have made many entire revolutions, so that the orbits
would have been completely mixed up.... A different explanation of
the group is given by the nebular hypothesis; so that Olbers's
hypothesis is no longer considered by astronomers."

247. _Later Discoveries of Asteroids._--Since 1845 over two hundred asteroids have been discovered. All these are so small, that it requires a very good telescope to see them; and even in very powerful telescopes they appear as mere points of light, which can be distinguished from the stars only by their motions.

To facilitate the discovery of these bodies, very accurate maps have been constructed, including all the stars down to the thirteenth magnitude in the neighborhood of the ecliptic. A reduced copy of one of these maps is shown in Fig. 271.

Furnished with a map of this kind, and with a telescope powerful enough to show all the stars marked on it, the observer who is searching for these small planets will place in the field of view of his telescope six spider-lines at right angles to each other, and at equal distances apart, in such a manner that several small squares will be formed, embracing just as much of the heavens as do those shown in the map. He will then direct his telescope to the region of the sky he wishes to examine, represented by the map, so as to be able to compare successively each square with the corresponding portion of the sky. Fig. 272 shows at the right hand the squares in the telescopic field of view, and at the left hand the corresponding squares of the map.

He can then assure himself if the numbers and positions of the stars mapped, and of the stars observed, are identical. If he observes in the field of view a luminous point which is not marked in the map, it is evident that either the new body is a star of variable brightness which was not visible at the time the map was made, or it is a planet, or perhaps a comet. If the new body remains fixed at the same point, it is the former; but, if it changes its position with regard to the neighboring stars, it is the latter. The motion is generally so sensible, that in the course of one evening the change of position may be detected; and it can soon be determined, by the direction and rate of the motion, whether the body is a planet or a comet.