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

by Robert S. Ball

Kepler also made another great discovery in connection with the same subject. If the planet moved in a circle with the sun in the centre, then there would be very good reason to expect that it would always move at the same speed, for there would be no reason why it should go faster at one place than at another. In fact, the planet would then be revolving always at the same distance from the sun, and every part of its path would be exactly like every other part. But when we consider that the motion is performed in an ellipse, so that the planet is curving round more rapidly at the extremities of its path than in the other parts where the curvature is less perceptible, we have no reason to expect that the speed shall remain the same all round.

We know that the engine-driver of a railway train always has to slacken speed when he is going round a sharp curve. If he did not do so, his train would be very likely to run off the line, and a dreadful accident would follow. The engine-driver is well aware that the conditions of pace are dependent on the curvature of his line. The planet finds that it, too, must pay attention to the curves; but the extraordinary point is that the planet acts exactly in the opposite way to the engine-driver. The planet puts on its highest pace at one of the most critical curves in the whole journey. There are two specially sharp curves in the planet’s path. These are, of course, the two extremities of the ellipse which it follows. The cautious engine-driver would, of course, creep round these with equal care, and no doubt the planet goes slowly enough about that end of the ellipse which is farthest from the sun. There its pace is slower than anywhere else; but from that moment onwards the planet steadily applies itself to getting up more and more speed. As it traverses the comparatively straight portion of the celestial road, the pace is ever accelerating until the sharp curve near the sun is being approached; then the velocity gets more and more alarming, until at last, in utter defiance of all rules of engine-driving, the planet rushes round one of the worst parts of the orbit at the highest possible speed. And yet no accident happens, though the planet has no nicely laid lines to keep it on the track.

If lines are necessary to save a railway train from destruction, how can we possibly escape when we have no similar assistance to keep us from flying away from the sun and off into infinite space? Kepler has taught us to measure the changes in the speed of the body with precision. He has shown that the planet must, at every point of its long journey, possess exactly the right speed; otherwise everything would go wrong. I dare say you have seen, at different points along a line of railway, boards put up here and there, with notices like, “Ten miles an hour.” These words are, of course, an intimation to the engine-driver that he is not to vary from the speed thus stated. Kepler has given us a law which is equivalent to a large number of caution boards, fixed all round the planet’s path, indicating the safe speed for the journey at every stage. It is fortunate for us that the planet is careful to observe these regulations. If the earth were to leave her track, the consequences would be far worse than those of the most frightful railway accident that ever happened. Whichever side we took would be almost equally disastrous. If we went inwards we should plunge into the sun, and if we went outwards we should be frozen by cold.

We owe our safety to the care with which the speed of the earth is prescribed. When near the sun, the earth is pulled inwards with exceptionally strong attraction. We are often told that when a strong temptation seizes us, the wisest thing that we can do is to run away as hard as possible. This is just what the laws of dynamics cause the earth to do at this critical time. She puts on her very best pace, and only slackens when she has got well away from the danger.

The peril that we are exposed to when the earth is at the other end of the orbit is of an opposite character. We are then a long way from the sun, and the pull which it can exercise upon the earth is correspondingly lessened. Care is then required lest we should escape altogether from the sun’s warmth and his guidance. We must therefore give time to the sun to exercise his power, so as to enable the earth to be recalled; accordingly we move as slowly as possible until the sun conquers the earth’s disposition to fly off, and we begin to return.

You may remember that when we were speaking about the moon, I showed you how a body might revolve around the earth in a circle under the influence of an attraction towards the earth’s centre. So long as the path is really a circle, then the power with which the earth is drawing the body remains the same. In a precisely similar way, a body could revolve around the sun in a circle, in which case also the attraction of the sun will remain the same all round. But now we have a very much more difficult case to consider. If the body does not always remain at the same distance, the power of the sun will not be the same at the different places. Whenever the object is near the sun, the attraction will be greater than when it is farther off. For example, when the distance between the two bodies is doubled, then the pull is reduced to the fourth part of what it was before.

THE DISCOVERIES MADE BY NEWTON.

I have now some great discoveries to talk to you about, which were made by Sir Isaac Newton. He was not an astronomer who looked much through a telescope, though he made many remarkable experiments. He used to sit in his study and think, and then he used to draw figures with his pencil, and make long calculations. At last he was able to give answers to the questions: What is the reason why the planet moves in an ellipse? Why should it move in this curve rather than in any other? Why should this ellipse be so placed that the sun lies at one of the foci?

If the planet had run uniformly round its course, Newton would have found his task an impossible one. But I have already explained that the motion is not uniform. I described how the planet hurried along with extra speed at certain parts of its path; how it lingered at other parts; how, in fact, it never preserved the same rate for even a single minute during the whole journey. Kepler had shown how to make a time-table for the whole journey. In fact, just as a captain on a long voyage keeps a record of each day’s run, and shows how to-day he makes 170 miles, and to-morrow perhaps 200, and the next day 210, while the day after he may fall back to 120, so Kepler gave rules by which the log of a planet in its voyage round the sun might be so faithfully kept that every day’s run would be accurately recorded.

When Newton commenced his work, one of the first questions he had to consider was the following: Suppose that a great globe like a planet, or a small globe like a marble, or an irregular body like an ordinary stone, were to be thrown into space, and were then to be left to follow its course without any force whatever acting upon it, where would it go to?