A Short History of Astronomy - Arthur Berry (read along books .txt) 📗

246. A few of Laplace’s numerical results as to the secular variations of the elements may serve to give an idea of the magnitudes dealt with.

The line of apses of each planet moves in the same direction; the most rapid motion, occurring in the case of Saturn, amounted to about 15″ per annum, or rather less than half a degree in a century. If this motion were to continue uniformly, the line of apses would require no less than 80,000 years to perform a complete circuit and return to its original position. The motion of the line of nodes (or line in which the plane of the planet’s orbit meets that of the ecliptic) was in general found to be rather more rapid. The annual alteration in the inclination of any orbit to the ecliptic in no case exceeded a fraction of a second; while the change of eccentricity of Saturn’s orbit, which was considerably the largest, would, if continued for four centuries, have only amounted to 1∕1000.

247. The theory of the secular inequalities has been treated at some length on account of the general nature of the results obtained. For the purpose of predicting the places of the planets at moderate distances of time the periodical inequalities are, however, of greater importance. These were also discussed very fully both by Lagrange and Laplace, the detailed working out in a form suitable for numerical calculation being largely due to the latter. From the formulæ given by Laplace and collected in the Mécanique Céleste several sets of solar and planetary tables were calculated, which were in general found to represent closely the observed motions, and which superseded the earlier tables based on less developed theories.152

248. In addition to the lunar and planetary theories nearly all the minor problems of gravitational astronomy were rediscussed by Laplace, in many cases with the aid of methods due to Lagrange, and their solution was in all cases advanced.

The theory of Jupiter’s satellites, which with Jupiter form a sort of miniature solar system but with several characteristic peculiarities, was fully dealt with; the other satellites received a less complete discussion. Some progress was also made with the theory of Saturn’s ring by shewing that it could not be a uniform solid body.

Precession and nutation were treated much more completely than by D’Alembert; and the allied problems of the irregularities in the rotation of the moon and of Saturn’s ring were also dealt with.

The figure of the earth was considered in a much more general way than by Clairaut, without, however, upsetting the substantial accuracy of his conclusions; and the theory of the tides was entirely reconstructed and greatly improved, though a considerable gap between theory and observation still remained.

The theory of perturbations was also modified so as to be applicable to comets, and from observation of a comet (known as Lexell’s) which had appeared in 1770 and was found to have passed close to Jupiter in 1767 it was inferred that its orbit had been completely changed by the attraction of Jupiter, but that, on the other hand, it was incapable of exercising any appreciable disturbing influence on Jupiter or its satellites.

As, on the one hand, the complete calculation of the perturbations of the various bodies of the solar system presupposes a knowledge of their masses, so reciprocally if the magnitudes of these disturbances can be obtained from observation they can be used to determine or to correct the values of the several masses. In this way the masses of Mars and of Jupiter’s satellites, as well as of Venus (§ 235), were estimated, and those of the moon and the other planets revised. In the case of Mercury, however, no perturbation of any other planet by it could be satisfactorily observed, and—except that it was known to be small—its mass remained for a long time a matter of conjecture. It was only some years after Laplace’s death that the effect produced by it on a comet enabled its mass to be estimated (1842), and the mass is even now very uncertain.

249. By the work of the great mathematical astronomers of the 18th century, the results of which were summarised in the Mécanique Céleste, it was shewn to be possible to account for the observed motions of the bodies of the solar system with a tolerable degree of accuracy by means of the law of gravitation.

Newton’s problem (§ 228) was therefore approximately solved, and the agreement between theory and observation was in most cases close enough for the practical purpose of predicting for a moderate time the places of the various celestial bodies. The outstanding discrepancies between theory and observation were for the most part so small as compared with those that had already been removed as to leave an almost universal conviction that they were capable of explanation as due to errors of observation, to want of exactness in calculation, or to some similar cause.

250. Outside the circle of professed astronomers and mathematicians Laplace is best known, not as the author of the Mécanique Céleste, but as the inventor of the Nebular Hypothesis.

This famous speculation was published (in 1796) in his popular book the Système du Monde already mentioned, and was almost certainly independent of a somewhat similar but less detailed theory which had been suggested by the philosopher Immanuel Kant in 1755.

Laplace was struck with certain remarkable characteristics of the solar system. The seven planets known to him when he wrote revolved round the sun in the same direction, the fourteen satellites revolved round their primaries still in the same direction,153 and such motions of rotation of sun, planets, and satellites about their axes as were known followed the same law. There were thus some 30 or 40 motions all in the same direction. If these motions of the several bodies were regarded as the result of chance and were independent of one another, this uniformity would be a coincidence of a most extraordinary character, as unlikely as that a coin when tossed the like number of times should invariably come down with the same face uppermost.

These motions of rotation and revolution were moreover all in planes but slightly inclined to one another; and the eccentricities of all the orbits were quite small, so that they were nearly circular.

Comets, on the other hand, presented none of these peculiarities; their paths were very eccentric, they were inclined at all angles to the ecliptic, and were described in either direction.

Moreover there were no known bodies forming a connecting link in these respects between comets and planets or satellites.154

From these remarkable coincidences Laplace inferred that the various bodies of the solar system must have had some common origin. The hypothesis which he suggested was that they had condensed out of a body that might be regarded either as the sun with a vast atmosphere filling the space now occupied by the solar system, or as a fluid mass with a more or less condensed central part or nucleus; while at an earlier stage the central condensation might have been almost non-existent.

Observations of Herschel’s (chapter XII., §§ 259-61) had recently revealed the existence of many hundreds of bodies known as nebulae, presenting very nearly such appearances as might have been expected from Laplace’s primitive body. The differences in structure which they shewed, some being apparently almost structureless masses of some extremely diffused substance, while others shewed decided signs of central condensation, and others again looked like ordinary stars with a slight atmosphere round them, were also strongly suggestive of successive stages in some process of condensation.

Laplace’s suggestion then was that the solar system had been formed by condensation out of a nebula; and a similar explanation would apply to the fixed stars, with the planets (if any) which surrounded them.

He then sketched, in a somewhat imaginative way, the process whereby a nebula, if once endowed with a rotatory motion, might, as it condensed, throw off a series of rings, and each of these might in turn condense into a planet with or without satellites; and gave on this hypothesis plausible reasons for many of the peculiarities of the solar system.

So little is, however, known of the behaviour of a body like Laplace’s nebula when condensing and rotating that it is hardly worth while to consider the details of the scheme.

That Laplace himself, who has never been accused of underrating the importance of his own discoveries, did not take the details of his hypothesis nearly as seriously as many of its expounders, may be inferred both from the fact that he only published it in a popular book, and from his remarkable description of it as “these conjectures on the formation of the stars and of the solar system, conjectures which I present with all the distrust (défiance) which everything which is not a result of observation or of calculation ought to inspire.”155