The fact appears to be, that though an enormous quantity of energy must have been lost by radiation from our system during the illimitable ages through which the evolution has been running its course, the disposable energy is not yet quite exhausted. There are certain adjustments in our system which may still be made and which will allow of yet further radiation of energy, while still preserving sufficient to keep up the necessary moment of momentum. It seems obvious that the system is tending towards a condition in which the planes of all the orbits shall be coincident, and in which all the directions shall be absolutely unanimous. If we were at once to alter the system by moving all the orbits into the plane of the ecliptic, but making no change in the dimensions of those orbits, or the velocities concerned; if we were also to adjust the rotations of the earth, as well as of the other planets, so that all the axes of rotation should be perpendicular to the plane of the ecliptic; if we were to turn the plane of the satellites of Uranus through that angle of 97°, which would suffice at the same time to bring it into coincidence with the ecliptic, and lay the movements of the satellites in the right direction; if we were also to turn the orbit of the satellite of Neptune through 145°, thus bringing that orbit to coincide with the plane of the ecliptic, in such a manner that the direction of the movement of the satellite of Neptune conspired with all the other movements of the system, then this rearrangement of the system would increase the moment of momentum, while the quantity of energy was not altered. But this is the same thing as saying that some energy yet remains to be disposed of, while the system still preserves the requisite moment of momentum.
The conclusion we come to may be thus expressed: the movements of the satellites of Uranus and Neptune do not disprove the nebular hypothesis. They rather illustrate the fact that the great evolution which has wrought the solar system into form has not yet finished its work; it is still in progress. The work is very nearly done, and when that work shall have been completed, the satellites of Uranus and Neptune will no longer be dissociated from the general concord.
CHAPTER XVIII.
THE BEGINNING OF THE NEBULA.
Nebula not of Infinite Duration—8,300 Coal-Units was the Total Energy of the System—460 Miles a Second—Solar Nebula from a Collision—What we Know as to the Colliding Bodies—Probability of Celestial Collisions—Multitudes of Dark Objects—New Star in Perseus—Characteristics of New Stars—Incandescent Hydrogen—The Ruby in the Spectrum—Photographs of the Spectrum—Rarity of a Collision on a Scale Adequate to a Solar System.
WHATEVER may have been the antiquity of the actual elements that formed the primæval nebula from which the solar system has been evolved, the nebula itself has certainly not been of infinite duration. The question then arises as to what has been the origin of the nebula as such, or rather by what agency the material from which the nebula was formed underwent so radical a transformation from its previous condition as to be changed into that glowing object which we have considered so frequently in this book. We have to explain how, by the operation of natural causes, a dark body can be transformed into a glowing nebula.
Let us first estimate what the quantity of energy in that system is. The sun has been pouring forth heat for inimitable ages, and will doubtless continue to pour forth heat for millions of years to come. But the destiny which awaits the sun, though it may be protracted, yet cannot be averted. The sun will go on pouring forth its heat and gradually shrinking. The time will come at last when the radius of the sun will have appreciably decreased, and when once it has assumed a density corresponding to a solid state its history as a radiant globe will be approaching its close. A period of insignificant extent, a century or less, will then suffice for that solid globe to cool down so as to be no longer an efficient source of light and heat. We shall assume that when the sun has ultimately become solid and cold, and when it is no longer the life and light of our system, it will have attained a mean density of 21.5, which we have chosen because that is the density of platinum, the heaviest substance known. In all probability the solar density will never become so great as this, but to include the most extreme case in our argument I am making the assumption in the form stated. We are now to estimate what will have been the total energy that the sun has radiated from the moment when as an indefinitely great nebula it first began to radiate at all, down to that moment in the future when, having shrunk to the density of platinum, and having parted with all its heat, the solar radiation is at an end.
In the beginning of the evolutionary history the sun was a nebula, which we have supposed to extend in every direction to an indefinitely great distance. The system has resulted from the contraction of that nebula, and the energy liberated in that contraction has supplied the sun’s radiation. We calculate (see Appendix) the energy that would be given out in the contraction of a nebula whose materials were originally at infinity, and which ultimately coalesced to form a cold, solid globe of the density of platinum, and as heavy as the sun. There is no object in attempting to express this quantity of energy in foot-pounds—the figures would convey no distinct impression—we shall employ the coal-unit explained in Chapter VI. We imagine a globe of coal the weight of the sun; then, if that globe of coal were adequately supplied with oxygen, it would, on combustion, give out a certain amount of heat, which is a convenient unit for our measurements. It is demonstrated that the quantity of energy given out by the contraction of the nebula from infinity, to this globe of the density of platinum, would be about equal to the quantity of energy which would be produced by the combustion of 8,300 globes of coal as heavy as the sun, an adequate contribution of oxygen being supposed to be supplied. This expresses the original endowment of energy in the solar system, or rather a major limit to that endowment; it shows that the solar system can never have developed more energy by contraction than that which could be produced by the combustion of 8,300 globes of coal as heavy as the sun. We may mention that of this great endowment of energy an amount which is rather less than half (3,400) has been already expended, so that rather more than half of the sun’s career as a radiant globe may yet have to be run.
We can also express the total energy of the solar system in a different manner. We shall consider what must be the velocity of the sun, so that the energy that it will possess, in virtue of that velocity, shall be equal to the energy which could be produced by the combustion of 8,300 globes of coal of the same weight. This calculation is very much simplified by making use of a principle which we have already stated and applied in Chapter V. We have shown that if a piece of coal be animated with a velocity of five miles a second, the energy it possesses in virtue of that motion is equal to the energy produced by the coal in the act of combustion. If a body were moving at the rate of, let us say, 100 miles a second—its speed being then twenty times as great as the particular speed just mentioned—its energy, which depends on the square of the velocity, would be 400 times as much as would be produced by the burning of a piece of coal equal to it in weight. We can easily calculate that if the sun were moving at a speed of 460 miles a second, it would possess, in virtue of its motion, as much energy as would be generated by the contraction of the primæval nebula from infinity down to a globe of the density of platinum.
It is thus easy to form a supposition as to how the nebula constituting our solar system may have come into being; most probably it originated in this way. Let us suppose that two masses, either dark or bright, either hot or of the temperature of space, or the temperature of frozen air, were moving with speeds of 460 miles a second. No doubt the velocities we are here postulating are very high velocities, but they are not unprecedentedly high. We know of stars which at this present moment move quite as fast, so that there is nothing unreasonable in our supposition so far as the velocities are concerned. Let us suppose that each of these bodies had a mass which is half that of our present solar system. If these two bodies dashed into collision, when moving from opposite directions, the effect of the blow would be to transform the energy into heat. That heat would be so great that it would be sufficient not alone to render these globes red-hot and white-hot, but even to fuse them—nay, further, to drive them into vapour, even to a vapour which might expand to an enormously great distance. In other words, it is quite conceivable that a collision of two such masses as we have here supposed might be adequate to the formation of a nebula such as that one which in the lapse of indefinite ages has shaped itself into the solar system.