The Evolution of Worlds

by Percival Lowell

In attempting now to discover how all this came about we notice first that the system could not have originated in the beautifully simple way suggested by Laplace, because of several impossibilities in the path. If rings were shed, as he supposed, from a symmetric contracting mass, they should have resulted in something even more symmetric than we observe to-day. In the next place they could not, it would appear, even if formed, have collected into planets.

Nor could there have been an original “fire-mist” with which as a stock in trade Laplace thriftily endowed his nebula to start with—the necessity for which has been likened to our supposed descent from monkeys; but which in truth is as misty a conception of the facts in the one case as it is a monkeying with them in the other. Darwin’s theory distinctly avers that we were not descended from monkeys; and Laplace’s fire-mist under modern examination evaporates away. It is an interesting outcome of modern analysis that the very fact which suggested the annular genesis of planets to Laplace, the rings of Saturn, should now probably be deemed a striking instance of the reverse. Far from its being an exemplar in the heavens of the pristine state of the solar system, we may now see in it a shining pattern of how the devolution of bodies comes about. For instead of typifying an unfortunate set of particles which untoward circumstance has prevented from coalescing into a single orb, it almost certainly represents the distraught state to which a once more compact congeries of them has been brought by planetary interference. For to just such fate must the stresses in it caused by Saturn have eventually led. Disruption inevitable to such a group the observation of comets demonstrates is daily taking place. When a comet passes round the Sun or near a planet, the partitive pulls of the body tend to dismember it, and the same is a fortiori true of matter circulating round a planet as relatively near as the meteoric particles that constitute Saturn’s rings. Starting as a congeries, it was pulled out more and more into a ring until it became practically even throughout. And the very action that produced it tends to keep it as surprisingly regular as we note to-day.

No, the planets probably were otherwise generated and may have looked in their earlier stages as the knots in the spiral nebulæ do to-day. But this does not mean that we can detail the process [[see NOTE 5]].

Taking now the congruities for guide, we proceed to see what they affirm or negative. Laplace, when he ventured on his exposition of the system of the world, did so “with the mistrust which everything which is not the direct outcome of observation or calculation must inspire.” To all who know how even figures can lie this caution will seem well timed. The best we can do to keep our heads steady is to lay firm hold at each step on the great underlying principles of physics. One of these is the conservation of the moment of momentum. This expression embodies one of the grandest generalizations of cosmic mechanics. The very phrase is fittingly sonorous, with something of that religious sublimity which the dear old lady said she found such a consolation in the biblical word Mesopotamia. Indeed the idea is grand for its very simplicity. Momentum means the quantity of motion in a body. It is the speed into the number of particles or the mass. Moment of momentum denotes the rotatory power of it round an axis. Now the curious and interesting thing about this quantity is that it can neither be diminished nor increased. It is an abstraction from which nothing can be abstracted—but results. It is the one unalterable thing in a universe of change. What it was in the beginning in a system, that it forever remains. Because of this unchangeableness we can use it very effectively for purposes of deduction. One of these is in connection with that other great principle of physics, the conservation of energy. By the mutual action of particles on one another, by contraction, by tidal pulls, and so on, some energy of motion is constantly being changed into heat and thus dissipated away. Energy of motion, therefore, is slowly being lost to the system, and the only stable state for the bodies composing it is when their energy of motion has decreased to the minimum consistent with the initial moment of momentum. This principle we shall find very fecund in its application. It means that our whole system is evolving in a way to lessen its energy of motion while keeping its quantity of motion unchanged. The universe always does a thing with the least possible expenditure of force and gets rid of its superfluous energy by parting with it to space. Philosophers may wrangle over its being the best possible of worlds, but it is incontrovertibly mechanically the laziest, which a pessimistic friend of mine says proves it the best.

Now this generalization finds immediate use in explaining certain features of the solar system. In looking over the congruities it will be seen that deviation from the principal plane of the system or departure from a circular orbit is always associated with smallness in size. The insignificant bodies are the erratic ones. Now it has been shown mathematically in several different ways that when small particles collect into a larger mass, the collisions tend to make the resultant orbit of the combination both more circular and more conformant to the general plane than its constituents. But we may see this more forthrightly by means of the general principle enunciated above. For in fact both results are direct outcomes of the conservation of moment of momentum. Given a certain moment of momentum for the system, the total energy of the bodies is least when they all move in one plane. This is evident at once because the components of motion at right angles to the principal plane add nothing to the moment of momentum of the system. It is also least when the bodies all revolve in circles about the centre of gravity. The circle has some interesting properties which almost justify the regard paid to it by the ancients as the only perfect figure. It encloses the maximum area for a given periphery, so that according to the old legends, if one were given as much land as he could enclose with a certain bull’s hide, he should, after cutting the hide into strips, arrange these along the circumference of a circle. Now this property of the circle is intimately connected with the fact that a body revolving in a circle has the greatest moment of momentum for the least expenditure of energy. For under the same central force all ellipses of the same longest diameters—major axes these are technically called—are described in the same time, and with the same energy, and of all such, the circle encloses the greatest area, which area measures the moment of momentum [[see NOTE 6]].

Given a certain moment of momentum, then the energy is least when the bodies all move in one plane and all travel in circles in that plane. As energy is constantly being dissipated while any alteration among the bodies is going on, to coplanarity and circularity of path all the bodies must tend, if by collision they be aggregated into larger masses. As in the present state of our system the small bodies travel out of the general plane in eccentric ellipses while the big ones travel in it in approximate circles, the facts indicate that the origin of the larger masses was due to development by aggregation out of smaller particles.

The next principle is of a different character. Half a century ago celestial mechanics dealt with bodies chiefly as points. The Earth was treated as a weighted point, and so was the Sun. This was possible because a sphere acts upon outside bodies as if all its mass were collected at its centre, and the Sun and many of the planets are practically spheres. But when it came to nicer questions of their present behavior and especially of their past career, it grew necessary to take their shape into account in their mutual effects. One of the results was the discovery of the great rôle played in evolution by tidal action. Inasmuch as the planets are not perfectly rigid bodies, each is subject to tidal deformation by the other, the outside being pulled more than the centre on one side and less on the other. Bodily tides are thus raised in it analogous to the surface tides we see in the ocean, only vastly greater, and these in turn act as a brake on its rotation.

Now the retrograde motions occurring in the outermost parts of all the systems, principal and subsidiary, only and always there: the retrograde rotations of Neptune and Uranus, the retrograde revolutions of the ninth satellite of Saturn and of the eighth of Jupiter, point to something fundamental. For when we consider that it is precisely in its outer portions that any forces shaping the development of the system have had less time to produce their effect, we perceive that apparent abnormality now is really survival of the original normal state, only to be found at present in what has not been sufficiently forced to change. It suggests that the pristine motion of the constituents of the scattered agglomerations which went to form the planets was retrograde, and that their present direct rotations and the direct revolutions of most of their satellites have been imposed by some force acting since. Let us inquire if there be a force competent to this end, and what its mode of action.

Let us see how tidal action would work. Tidal force would raise bulges, and these, not being carried round with the planet’s rotation except to a certain distance, due to viscosity, must necessarily act as brakes upon the planet’s spin. In consequence of the friction they would thus exert, energy of motion must be lost. So long, then, as tidal forces can come into play, the energy of the system is capable of decrease. According to the last principle we considered, the system cannot be in stable equilibrium until this superfluous energy is lost or until tidal forces become inoperative, which cannot be till all the bodies in the system turn the same face to their respective centres of attraction.

To see this more clearly, take the case of a retrograde spin of a planet as compared with a direct one. The energy of the planet’s spin is the same in both cases, because energy depends on the square of a quantity; to wit, that of the velocity, and is therefore independent of sign. Not so the moment of momentum. For this depends on the first power of the speed, and if positive in the one case, must be negative in the other. The moment of momentum of the whole system, then, is less in the former case, since the moment of momentum of the retrograde rotation must be subtracted from, that of the direct rotation be added to, that of the rest of the system. For a given initial moment of momentum with which the system was endowed at the start, there is, then, superfluous energy in the first state which can be got rid of through reduction to the second. Nature, according to her principles of least exertion, avails herself of the chance of dispensing with it, and a direct rotation results. Sir Robert Ball first suggested this argument.