Fig. 50.—I. A Natural System on the Left.
II. An Unnatural System on the Right.
There can be no doubt that either of these two systems would be possible for thousands of revolutions. There is nothing whatever to prevent A and B from being started in the same direction round the sun as in the first figure, or with A in one direction and B in the opposite direction, as in the second figure. It is equally conceivable that, while A and B revolve in the same direction, both should be opposite to that of the sun. But one system is permanent, and the other is not.
For, as a matter of fact, we do not find in Nature such an arrangement as that in the second figure, or as that in which both the planets revolve in opposite directions to the sun’s rotation; what we do find is, that the planets go round in the same direction as the sun. And the explanation is undoubtedly connected with the important principle already illustrated, namely, that natural systems are in a condition in which the total quantity of energy undergoes continuous reduction in comparison with the moment of momentum.
In the arrangements made in the two figures, it will be recollected that the masses of the three bodies were respectively the same, and also their distances apart, and their velocities. As the energy depends only on the masses, the distances, and the velocities, the energies of the two systems must be identical. But the moment of momentum of the two systems is very different, for while in the one case the sum of the moments of momentum of the sun’s rotation and that of the planet A, which is going in the same direction, are to be increased by the moment of momentum of B, the same is not the case in the other system. The moment of momentum of the sun and of A conspire, no doubt, and must be added together; but as B is revolving in the opposite direction, the moment of momentum of this planet has to be subtracted before we obtain the nett moment of momentum of the system. Hence, we perceive a remarkable difference between the two systems; for, though in each the total energy is the same, yet in the latter case the moment of momentum is smaller than in the former.
It has been pointed out that the effect of the mutual actions of the different bodies of a system is to lessen, in course of time, the total quantity of energy that they receive in the beginning, while it is not in the power of the mutual actions of the particles of the system to affect the sum total of the moment of momentum. Hence we see that, so long as the system is isolated from external interference, the tendency must ever be towards the reduction of the quantity of energy to as low a point as may be compatible with the preservation of the necessary amount of moment of momentum. The first of the two systems given in Fig. [50] is much more in conformity with this principle than the second. The moment of momentum in the former case must be nearly as large as could be obtained by any other disposition of the matter forming it, with the same amount of energy. But in the second diagram the moment of momentum is much less, though the energy is the same. It follows that the energy of this system might be largely reduced, for if accompanied by a suitable rearrangement of the planets the reduced amount of moment of momentum might be easily provided for. We thus see that this system is not one to which the evolution of a material arrangement would ultimately tend. It is, therefore, not to be expected in Nature, and we do not find it. Of course, the same would be equally true if, instead of having merely two planets, as I have here supposed for the sake of illustration, the planets were much more numerous. The operation of the causes we have been considering will show that, in the evolution of such a system, there will be a tendency for the planets to revolve in the same direction.
It is easy to see how, in the contraction of the original nebula, there must have been a strong influence to check and efface any movements antagonistic to the general direction of the rotation of the nebula. If particles revolve in a direction opposite to the current pursued by the majority of particles, there would be collisions and frictions, and these collisions and frictions will, of course, find expression in the production of equivalent quantities of heat. That heat will, in due course, be radiated away at the expense of the energy of the system, and consequently, so long as any contrary movements exist, there will be an exceptional loss of energy from this cause. Thus the energy would incessantly tend to decline. As the shrinking of the body proceeded while the moment of momentum would have to be sustained, this would incessantly tend more and more to require from all the particles a movement in the same direction.
The second concord of the planetary system, which is implied in the fact that all the planets go round in the same direction, need not therefore surprise us. It is a consequence, an inevitable consequence, of the evolution of that system from the great primæval nebula. We have seen that it would be excessively improbable that even nine or ten planets should revolve round the sun in the same direction, if the directions of their movements had been merely decided by chance. We have seen that the movements of the hosts of planets, which actually form our system, would be inconceivable, unless there were some reason for those movements. The chances against such an arrangement having arisen without some predisposing cause is so vast that, even if the chances were infinite, the case would be hardly strengthened. But once we grant that the system originated from the contraction of the primæval nebula, dynamics offers ready aid, and the difficulty vanishes. Not only do we see most excellent reasons why all the planets should revolve in the same direction; we are also provided with illustrations of similar evolutions in progress in other parts of the universe; we learn that the evolving nebula, however erratic may have been its primitive motion, whatever cross currents may have agitated it in the early phases of a possibly violent origin, will ultimately attain a rotation uniform in direction. As the evolution proceeds, the various parts of the nebula draw together to form the planets of the future system, and the planets retain the movement possessed by their component particles. Thus we see that the nebular theory not only extricates us from the difficulty of trying to explain something which seemed almost infinitely improbable, but it also shows why no other disposition of the motions than that which we actually find could be expected. The nebular theory explains to us why there is no exception to that fundamental law in the solar system which declares that the orbits of the planets shall all be followed in the same direction.
This wonderful agreement in the movements of the planets, which we have called the second concord, thus affords us striking evidence of the general truth of the nebular theory. But there is yet a third concord in the solar system which, like the other two, lends wonderful corroboration to the sublime doctrine of Kant and Laplace. This we shall consider in the next chapter.