A Text-Book of Astronomy

by George C. Comstock

Thus, as we attempt to trace the sun's history into the past, the farther back we go the greater shall we expect to find its diameter and the greater the space (volume) through which its molecules are spread. By reason of this expansion its density must have been less then than now, and by going far enough back we may even reach a time at which the density was comparable with what we find in the nebulæ of to-day. If our ideas of the sun's present mechanism are sound, then, as a necessary consequence of these, its past career must have been a process of condensation in which its component particles were year by year packed closer together by their own attraction for each other. As we have seen in [§ 126], this condensation necessarily developed heat, a part of which was radiated away as fast as produced, while the remainder was stored up, and served to raise the temperature of the sun to what we find it now. At the present time this temperature is a chief obstacle to further shrinkage, and so powerfully opposes the gravitative forces as to maintain nearly an equilibrium with them, thus causing a very slow rate of further condensation. But it is not probable that this was always so. In the early stages of the sun's history, when the temperature was low, contraction of its bulk must have been more rapid, and attempts have been made by the mathematicians to measure its rate of progress and to determine how long a time has been consumed in the development of the present sun from a primitive nebulous condition in which it filled a space of greater diameter than Neptune's orbit. Of course, numerical precision is not to be expected in results of this kind, but, from a consideration of the greatest amount of heat that could be furnished by the shrinkage of a mass equal to that of the sun, it seems that the period of this development is to be measured in tens of millions or possibly hundreds of millions of years, but almost certainly does not reach a thousand millions.

229. The sun's future.—The future duration of the sun as a source of radiant energy is surely to be measured in far smaller numbers than these. Its career as a dispenser of light and heat is much more than half spent, for the shrinkage results in an ever-increasing density, which makes its gaseous substance approximate more and more toward the behavior of a liquid or solid, and we recall that these forms of matter can not by any further condensation restore the heat whose loss through radiation caused them to contract. They may continue to shrink, but their temperature must fall, and when the sun's substance becomes too dense to obey the laws of gaseous matter its surface must cool rapidly as a consequence of the radiation into surrounding space, and must congeal into a crust which, although at first incandescent, will speedily become dark and opaque, cutting off the light of the central portions, save as it may be rent from time to time by volcanic outbursts of the still incandescent mass beneath. But such outbursts can be of short duration only, and its final condition must be that of a dark body, like the earth or moon, no longer available as a source of radiant energy. Even before the formation of a solid crust it is quite possible that the output of light and heat may be seriously diminished by the formation of dense vapors completely enshrouding it, as is now the case with Jupiter and Saturn. It is believed that these planets were formerly incandescent, and at the present time are in a state of development through which the earth has passed and toward which the sun is moving. According to Newcomb, the future during which the sun can continue to furnish light and heat at its present rate is not likely to exceed 10,000,000 years.

This idea of the sun as a developing body whose present state is only temporary, furnishes a clew to some of the vexing problems of solar physics. Thus the sun-spot period, the distribution of the spots in latitude, and the peculiar law of rotation of the sun in different latitudes, may be, and very probably are, results not of anything now operating beneath its photosphere, but of something which happened to it in the remote past—e. g., an unsymmetrical shrinkage or possibly a collision with some other body. At sea the waves continue to toss long after the storm which produced them has disappeared, and, according to the mathematical researches of Wilsing, a profound agitation of the sun's mass might well require tens of thousands, or even hundreds of thousands of years to subside, and during this time its effects would be visible, like the waves, as phenomena for which the actual condition of things furnishes no apparent cause.

230. The nebular hypothesis.—The theory of the sun's progressive contraction as a necessary result of its radiation of energy is comparatively modern, but more than a century ago philosophic students of Nature had been led in quite a different way to the belief that in the earlier stages of its career the sun must have been an enormously extended body whose outer portions reached even beyond the orbit of the remotest planet. Laplace, whose speculations upon this subject have had a dominant influence during the nineteenth century, has left, in a popular treatise upon astronomy, an admirable statement of the phenomena of planetary motion, which suggest and lead up to the nebular theory of the sun's development, and in presenting this theory we shall follow substantially his line of thought, but with some freedom of translation and many omissions.

He says: "To trace out the primitive source of the planetary movements, we have the following five phenomena: (1) These movements all take place in the same direction and nearly in the same plane. (2) The movements of the satellites are in the same direction as those of the planets. (3) The rotations of the planets and the sun are in the same direction as the orbital motions and nearly in the same plane. (4) Planets and satellites alike have nearly circular orbits. (5) The orbits of comets are wholly unlike these by reason of their great eccentricities and inclinations to the ecliptic." That these coincidences should be purely the result of chance seemed to Laplace incredible, and, seeking a cause for them, he continues: "Whatever its nature may be, since it has produced or controlled the motions of the planets, it must have reached out to all these bodies, and, in view of the prodigious distances which separate them, the cause can have been nothing else than a fluid of great extent which must have enveloped the sun like an atmosphere. A consideration of the planetary motions leads us to think that ... the sun's atmosphere formerly extended far beyond the orbits of all the planets and has shrunk by degrees to its present dimensions." This is not very different from the idea developed in [§ 228] from a consideration of the sun's radiant energy; but in Laplace's day the possibility of generating the sun's heat by contraction of its bulk was unknown, and he was compelled to assume a very high temperature for the primitive nebulous sun, while we now know that this is unnecessary. Whether the primitive nebula was hot or cold the shrinkage would take place in much the same way, and would finally result in a star or sun of very high temperature, but its development would be slower if it were hot in the beginning than if it were cold.

But again Laplace: "How did the sun's atmosphere determine the rotations and revolutions of planets and satellites? If these bodies had been deeply immersed in this atmosphere its resistance to their motion would have made them fall into the sun, and we may therefore conjecture that the planets were formed, one by one, at the outer limits of the solar atmosphere by the condensation of zones of vapor which were cast off in the plane of the sun's equator." Here he proceeds to show by an appeal to dynamical principles that something of this kind must happen, and that the matter sloughed off by the nebula in the form of a ring, perhaps comparable to the rings of Saturn or the asteroid zone, would ultimately condense into a planet, which in its turn might shrink and cast off rings to produce satellites.

Planets and satellites would then all have similar motions, as noted at the beginning of this section, since in every case this motion is an inheritance from a common source, the rotation of the primitive nebula about its own axis. "All the bodies which circle around a planet having been thus formed from rings which its atmosphere successively abandoned as rotation became more and more rapid, this rotation should take place in less time than is required for the orbital revolution of any of the bodies which have been cast off, and this holds true for the sun as compared with the planets."

231. Objections to the nebular hypothesis.—In Laplace's time this slower rate of motion was also supposed to hold true for Saturn's rings as compared with the rotation of Saturn itself, but, as we have seen in [Chapter XI], this ring is made up of a great number of independent particles which move at different rates of speed, and comparing, through Kepler's Third Law, the motion of the inner edge of the ring with the known periodic time of the satellites, we may find that these particles must rotate about Saturn more rapidly than the planet turns upon its axis. Similarly the inner satellite of Mars completes its revolution in about one third of a Martian day, and we find in cases like this grounds for objection to the nebular theory. Compare also Laplace's argument with the peculiar rotations of Uranus, Neptune, and their satellites ([Chapter XI]). Do these fortify or weaken his case?