Star-land: Being Talks With Young People About the Wonders of the Heavens

by Robert S. Ball

Fig. 58.—To illustrate the First Law of Motion.

I would recommend you to learn this by heart. I can assure you it is quite as well worth knowing as those rules in the Latin Grammar with which many of you, I have no doubt, are acquainted. The best proof of the first law of motion is derived, not from any experiments, but from astronomy. We make many calculations about the movements of the sun, the moon, the stars, and then we venture on predictions, and we find those predictions verified. Thus we had a transit of Venus across the sun in 1882, and every astronomer knew that this was going to occur, and many went to the ends of the earth so that they might see it favorably. Their anticipations were realized; they always are. Astronomers make no mistakes in these matters. They know that there will be another transit of Venus in the year 2004, but not sooner. The calculations by which these accurate prophecies are made involve this first law of motion; and as we find that such prophecies are always fulfilled, we know that the first law of motion must be true also.

Newton knew that if a planet were merely left alone in space, it would continue to move on forever in a straight line. But Kepler had shown that the planet did not move in a straight line, but that it described an ellipse. One conclusion was obvious. There must be some force acting upon the planet which pulls it away from the straight line it would otherwise pursue. We may, for the sake of illustration, imagine this force to be applied by a rope attached to the planet so that at every moment it is dragged by some unseen hand. To find the direction this rope must have, we take the law of Kepler, which explains the rules according to which the planet varies its speed. I cannot enter into the question fully, as it would be too difficult for us to discuss now. I should have to talk a great deal more about mathematics than would be convenient just at present; but I think you can all understand the result to which Newton was led. He showed that the rope must always be directed towards the sun. In other words, suppose that there was no sun, but that in the place which it occupied there was a strong enough giant constantly pulling away at the planet, then we should find that the speed of the planet would alter just in the way it actually does. Thus we learn that some force must reside in the sun by which the planet is drawn, and this force is exerted, although there is no visible bond between the sun and the planet.

There is another fact to be learned about the sun’s attraction, and this time we obtain it by knowing the shape of the curve followed by the planet. The laws by which the planet’s speed is regulated prove that the force emanates from the sun. We shall now learn much more when we take into account that the path of the planet is an ellipse, of which the sun lies at the focus. Nothing has been said as yet regarding the magnitude of the pull which is being exerted by the sun. Is that pull to be always the same, or is it to be greater at some times than at other times? Newton showed that no ellipse other than a circle could be described, if the pull from the sun were always the same. Its magnitude must be continually changed, and the nearer the planet lies to the sun, the more vehement is the pull it receives. Newton laid down the exact law by which the force on the planet at any one place in its path could be compared with the force at any other position. Let us suppose that the planet is in a certain position, and that it then passes into a second position, which is twice as far from the sun. The pull upon the planet at the shorter distance is not only greater than the pull at the longer distance, but it is actually four times as much. Stating this result a little more generally, we assert, in the language of astronomers, that the attraction varies inversely as the square of the distance. If this law were departed from, then I do not say that it would be impossible for the planet to revolve around the sun in some fashion, but the motion would not be performed in an ellipse described around the sun in the focus.

You see how very instructive are the laws which Kepler discovered. From the first of them we were able to infer that the sun attracts the planets; from the second, we have learned how the magnitude of the attracting force varies.

The true importance of these great discoveries will be manifest when we compare them with what we have already learned with regard to the movements of the moon. As the moon revolves around the earth it is held by the earth’s attraction, and the moon follows a path which, though nearly a circle, is really an ellipse. This orbit is described around the earth just as the earth describes its path around the sun. That law by which a stone falls to the ground in consequence of the earth’s attraction is merely an illustration of a great general principle. Every body in the whole universe attracts every other body.

Think of two weights lying on the table. They no doubt attract each other, but the force is an extremely small one—so small, indeed, that you could not measure it by any ordinary appliance. One or both of the attracting masses must be enormously big if their mutual gravitation is to be readily appreciable. The attraction of the earth on a stone is a considerable force, because the earth is so large, even though the stone may be small. Imagine a pair of colossal solid iron cannon-balls, each 53 yards in diameter, and weighing about 417,000 tons. Suppose these two globes were placed a mile apart, the pull of one of them on the other by gravitation would be just a pound weight. Notwithstanding the size of these masses, the hand of a child could prevent any motion of one ball by the attraction of the other. If, however, they were quite free to move, and there was absolutely no friction, the balls would begin to draw together; at first they would creep so slowly that the motion would hardly be noticed. The pace would no doubt continue to improve slowly, but still not less than three or four days must elapse before they will have come together.

By the kindness of Professor Dewar, I am enabled to exhibit a contrivance with which we can illustrate the motion of a planet around the sun. Here is a long wire suspended from the roof of this theatre, and attached to its lower end is an iron ball, made hollow for the sake of lightness. When I draw the ball aside, it swings to and fro with the regularity of a great pendulum. But when I place a powerful magnet in its neighborhood ([Fig. 59]), you see that as soon as the ball gets near the magnet it is violently drawn to one side, and follows a curved path. This magnet may be taken to represent the sun, while the ball is like our earth, or any other planet, which would move in a straight line were it not for the attraction of the sun which draws the body aside.