The Earth's Beginning

by Robert S. Ball

Fig. 49.—Orbits of Earth, Eros and Mars.

We may illustrate this remarkable coincidence in the following manner: Suppose we take ten coins in the hand, and toss them all up together and let them fall on the table; in the vast majority of cases in which the experiment may be tried, there would be some heads and some tails; they would not all be heads. But it is, of course, not impossible that the coins should all turn up heads. We should, however, deem it a very remarkable circumstance if it happened: yet it would certainly not be more remarkable than that the ten celestial movements should all take place in the same direction, unless, indeed, it should turn out that there is some sound physical cause which imposes on the planets of the solar system an obligation, restricting their movements round the sun to the same direction as that in which the sun itself rotates.

It will be useful to study the matter numerically; and the rules of probabilities will enable us to do so, as we may see by the following illustration: We deem the captain of a cricket team fortunate when he wins the toss for innings. We should deem him lucky indeed if he won it three times in successive matches. If he won it five times running, his luck would be phenomenal; while, if it was stated that he won it ten times consecutively, we should consider the statement well-nigh incredible. For it is easy to calculate that the chances against such an occurrence are one thousand and twenty-four to one. In like manner we may say, that for nine planets and the sun all to go round in the same direction would be indeed surprising if the arrangement of the planets had been determined by chance; there are more than a thousand chances to one against such an occurrence.

But Ceres was only the earliest of many other similar discoveries. And as each asteroid was successively brought to light, it became most interesting to test whether it followed the rest of the planets in that wonderful unanimity in the direction of their movements of revolution, or whether it made a new departure by going in the opposite direction. No such exception has ever yet been observed. Let us take, then, ten more planets, in addition to those we have already considered, so that we have now nineteen planets all revolving in the same direction as the sun rotates. It is easy to compute the improbability that these twenty movements should all be in the same direction, if, indeed, it were by chance that their directions had been determined. It is the same problem as the following: What is the chance that twenty coins, taken together in the hand and tossed into the air at once, shall all alight with their heads uppermost? We have seen that the chances against this occurrence, if there were ten coins, is about a thousand to one. It can easily be shown that if there were twenty coins the chances against the occurrence would be a million to one. We thus see that, even with no more than nineteen planets and the sun, there is a million to one against a unanimity in the directions of the movements, if the determination of the motions was made by chance. We may, however, express the result in a different manner, which is more to the purpose of our argument. There are a million chances to one in favour of the supposition that the disposition of the movements of the planets has not been the result of chance; or we may say that there are a million chances to one in favour of the supposition that some physical agent has caused the unanimity.

We can add almost any desired amount of numerical strength to the argument. The discoveries of minor planets went on with ever-increasing success through the whole of the last century. When ten more had been found, and when each one was shown to obey the same invisible guide as to the direction in which it should pursue its elliptic orbit, the chances in favour of some physical cause for the unanimity became multiplied by yet another thousand. The probability then stood at a thousand millions to one. As the years rolled by, asteroids were found in ever-increasing abundance. Sometimes a single astronomer discovered two, and sometimes even more than two, on a single night. In the course of a lifetime a diligent astronomer has placed fifty discoveries of asteroids, or even more than fifty, on his record. By combined efforts the tale of the asteroids has now approached five hundred, and out of that huge number of independent planetary bodies there is not one single dissentient in the direction of its motion. Without any exception whatever, they all perform their revolutions in the same direction as the sun rotates at the centre. When this great host is considered, the numerical strength of the argument would require about 150 figures for expression. Each new asteroid simply doubled the strength of the argument as it stood before.

Professor J. J. Thomson recently discovered that there are corpuscles of matter very much smaller than atoms. Let us think of one of these corpuscles, of which many millions would be required to make the smallest grain of sand which would just be visible under a microscope. Think, on the other hand, of a sphere extending through space to so vast a distance that every star in the Milky Way will be contained within its compass. Then the number of those corpuscles which would be required to fill that sphere is still far too small to represent the hugeness of the improbability that all the five hundred planetary bodies should revolve in the same direction, if chance, and chance alone, had guided the direction which each planet was to pursue in moving round its orbit.

The mere statement of these facts is sufficient to show that some physical agent must have caused this marvellous concord in the movements of the solar system. How the argument would have stood if there had been even a single dissentient it is not necessary to consider, for there is no dissentient No reasonable person will deny that these facts impose an obligation to search for the physical explanation of this feature in the planetary movements.

As in the last chapter, where we were dealing with the positions of the planes of the orbits, there can here be no hesitation as to the true cause of this most striking characteristic of the planetary movements. The nebular theory is at once ready with an explanation, as has been already indicated in Chapter XI. The primæval nebula, endowed in the beginning with a certain amount of moment of momentum, has been gradually contracting. It has been gradually expending its energy, as we have already had occasion to explain; but the moment of momentum has remained undiminished. And from this it can be shown that the dynamical principles guiding the evolution of the nebula must ultimately refuse permission for any planet to revolve in opposition to the general movement. This point is a very interesting one, and as it is of very great importance in connection with our system, I must give it some further illustration and explanation.

The two figures that are shown in Fig. [50] represent two imaginary systems. We have a sun in each, and we have two planets in each. The sun is marked with the letter S, and the two planets are designated by A and B. For simplicity I have represented the orbits as circles, and for the same reason I have left out the rest of the planets; we shall also suppose the orbits of the two planets that are involved to lie exactly in the same plane. In the two systems that I have here supposed, the two suns are to be of the same weight, the planet A in one system is of equal mass to the planet A in the other; and the planets B in the two systems are also equal. It is also assumed that the orbit of A in one diagram shall be the same as the orbit of A in the other, and that the orbit of B in one shall be precisely the same as the orbit of B in the other. The sun rotates in precisely the same manner in both, and takes the same time for each rotation. A, in one system, goes round in the same time that A does in the other; and B, in one system, goes round in the same time that B does in the other. There is, therefore, a perfect resemblance between the two systems I have here supposed in every point but one. I have indicated, as usual, the movements of the bodies by arrows, and, while in one of the systems the sun and A and B all go round in the same direction, in the other system the sun and A go round, no doubt, in the same direction, but the direction of B is opposite. We are not, in this illustration, considering the rotations of the planets on their axes. That will be dealt with in the next chapter.