In the case of the particular propositions in question the progress of astronomy and physics has thrown a good deal of emphasis on some of the points in which the assumptions required by Lagrange and Laplace are not satisfied by the actual solar system.
It was assumed for the purposes of the stability theorems that the bodies of the solar system are perfectly rigid; in other words, the motions relative to one another of the parts of any one body were ignored. Both the ordinary tides of the ocean and the bodily tides to which modern research has called attention were therefore left out of account. Tidal friction, though at present very minute in amount ([§ 287]), differs essentially from the perturbations which form the main subject-matter of gravitational astronomy, inasmuch as its action is irreversible. The stability theorems shewed in effect that the ordinary perturbations produced effects which sooner or later compensated one another, so that if a particular motion was accelerated at one time it would be retarded at another; but this is not the case with tidal friction. Tidal action between the earth and the moon, for example, gradually lengthens both the day and the month, and increases the distance between the earth and the moon. Solar tidal action has a similar though smaller effect on the sun and earth. The effect in each case—as far as we can measure it at all—seems to be minute almost beyond imagination, but there is no compensating action tending at any time to reverse the process. And on the whole the energy of the bodies concerned is thereby lessened. Again, modern theories of light and electricity require space to be filled with an “ether” capable of transmitting certain waves; and although there is no direct evidence that it in any way affects the motions of earth or planets, it is difficult to imagine a medium so different from all known forms of ordinary matter as to offer no resistance to a body moving through it. Such resistance would have the effect of slowly bringing the members of the solar system nearer to the sun, and gradually diminishing their times of revolution round it. This is again an irreversible tendency for which we know of no compensation.
In fact, from the point of view which Lagrange and Laplace occupied, the solar system appeared like a clock which, though not going quite regularly, but occasionally gaining and occasionally losing, nevertheless required no winding up; whereas modern research emphasises the analogy to a clock which after all is running down, though at an excessively slow rate. Modern study of the sun’s heat ([§ 319]) also indicates an irreversible tendency towards the “running down” of the solar system in another way.
294. Our account of modern descriptive astronomy may conveniently begin with planetary discoveries.
The first day of the 19th century was marked by the discovery of a new planet, known as Ceres. It was seen by Giuseppe Piazzi (1746-1826) as a strange star in a region of the sky which he was engaged in mapping, and soon recognised by its motion as a planet. Its orbit—first calculated by Gauss ([§ 276])—shewed it to belong to the space between Mars and Jupiter, which had been noted since the time of Kepler as abnormally large. That a planet should be found in this region was therefore no great surprise; but the discovery by Heinrich Olbers (1758-1840), scarcely a year later (March 1802), of a second body (Pallas), revolving at nearly the same distance from the sun, was wholly unexpected, and revealed an entirely new planetary arrangement. It was an obvious conjecture that if there was room for two planets there was room for more, and two fresh discoveries (Juno in 1804, Vesta in 1807) soon followed.
Fig. 88.—Photographic trail of a minor planet.
[To face p. 377.
The new bodies were very much smaller than any of the other planets, and, so far from readily shewing a planetary disc like their neighbours Mars and Jupiter, were barely distinguishable in appearance from fixed stars, except in the most powerful telescopes of the time; hence the name asteroid (suggested by William Herschel) or minor planet has been generally employed to distinguish them from the other planets. Herschel attempted to measure their size, and estimated the diameter of the largest at under 200 miles (that of Mercury, the smallest of the ordinary planets, being 3000), but the problem was in reality too difficult even for his unrivalled powers of observation. The minor planets were also found to be remarkable for the great inclination and eccentricity of some of the orbits; the path of Pallas, for example, makes an angle of 35° with the ecliptic, and its eccentricity is 1∕4, so that its least distance from the sun is not much more than half its greatest distance. These characteristics suggested to Olbers that the minor planets were in reality fragments of a primeval planet of moderate dimensions which had been blown to pieces, and the theory, which fitted most of the facts then known, was received with great favour in an age when “catastrophes” were still in fashion as scientific explanations.