The Story of the Heavens

by Robert S. Ball

Such are the three celebrated laws of Planetary Motion, which have always been associated with the name of their discoverer. The profound skill by which these laws were elicited from the mass of observations, the intrinsic beauty of the laws themselves, their widespread generality, and the bond of union which they have established between the various members of the solar system, have given them quite an exceptional position in astronomy.

As established by Kepler, these planetary laws were merely the results of observation. It was found, as a matter of fact, that the planets did move in ellipses, but Kepler assigned no reason why they should adopt this curve rather than any other. Still less was he able to offer a reason why these bodies should sweep over equal areas in equal times, or why that third law was invariably obeyed. The laws as they came from Kepler's hands stood out as three independent truths; thoroughly established, no doubt, but unsupported by any arguments as to why these movements rather than any others should be appropriate for the revolutions of the planets.

It was the crowning triumph of the great law of universal gravitation to remove this empirical character from Kepler's laws. Newton's grand discovery bound together the three isolated laws of Kepler into one beautiful doctrine. He showed not only that those laws are true, but he showed why they must be true, and why no other laws could have been true. He proved to demonstration in his immortal work, the "Principia," that the explanation of the famous planetary laws was to be sought in the attraction of gravitation. Newton set forth that a power of attraction resided in the sun, and as a necessary consequence of that attraction every planet must revolve in an elliptic orbit round the sun, having the sun as one focus; the radius of the planet's orbit must sweep over equal areas in equal times; and in comparing the movements of two planets, it was necessary to have the squares of the periodic times proportional to the cubes of the mean distances.

As this is not a mathematical treatise, it will be impossible for us to discuss the proofs which Newton has given, and which have commanded the immediate and universal acquiescence of all who have taken the trouble to understand them. We must here confine ourselves only to a very brief and general survey of the subject, which will indicate the character of the reasoning employed, without introducing details of a technical character.

Let us, in the first place, endeavour to think of a globe freely poised in space, and completely isolated from the influence of every other body in the universe. Let us imagine that this globe is set in motion by some impulse which starts it forward on a rapid voyage through the realms of space. When the impulse ceases the globe is in motion, and continues to move onwards. But what will be the path which it pursues? We are so accustomed to see a stone thrown into the air moving in a curved path, that we might naturally think a body projected into free space will also move in a curve. A little consideration will, however, show that the cases are very different. In the realms of free space we find no conception of upwards or downwards; all paths are alike; there is no reason why the body should swerve to the right or to the left; and hence we are led to surmise that in these circumstances a body, once started and freed from all interference, would move in a straight line. It is true that this statement is one which can never be submitted to the test of direct experiment. Circumstanced as we are on the surface of the earth, we have no means of isolating a body from external forces. The resistance of the air, as well as friction in various other forms, no less than the gravitation towards the earth itself, interfere with our experiments. A stone thrown along a sheet of ice will be exposed to but little resistance, and in this case we see that the stone will take a straight course along the frozen surface. A stone similarly cast into empty space would pursue a course absolutely rectilinear. This we demonstrate, not by any attempts at an experiment which would necessarily be futile, but by indirect reasoning. The truth of this principle can never for a moment be doubted by one who has duly weighed the arguments which have been produced in its behalf.

Admitting, then, the rectilinear path of the body, the next question which arises relates to the velocity with which that movement is performed. The stone gliding over the smooth ice on a frozen lake will, as everyone has observed, travel a long distance before it comes to rest. There is but little friction between the ice and the stone, but still even on ice friction is not altogether absent; and as that friction always tends to stop the motion, the stone will at length be brought to rest. In a voyage through the solitudes of space, a body experiences no friction; there is no tendency for the velocity to be reduced, and consequently we believe that the body could journey on for ever with unabated speed. No doubt such a statement seems at variance with our ordinary experience. A sailing ship makes no progress on the sea when the wind dies away. A train will gradually lose its velocity when the steam has been turned off. A humming-top will slowly expend its rotation and come to rest. From such instances it might be plausibly argued that when the force has ceased to act, the motion that the force generated gradually wanes, and ultimately vanishes. But in all these cases it will be found, on reflection, that the decline of the motion is to be attributed to the action of resisting forces. The sailing ship is retarded by the rubbing of the water on its sides; the train is checked by the friction of the wheels, and by the fact that it has to force its way through the air; and the atmospheric resistance is mainly the cause of the stopping of the humming-top, for if the air be withdrawn, by making the experiment in a vacuum, the top will continue to spin for a greatly lengthened period. We are thus led to admit that a body, once projected freely in space and acted upon by no external resistance, will continue to move on for ever in a straight line, and will preserve unabated to the end of time the velocity with which it originally started. This principle is known as the first law of motion.

Let us apply this principle to the important question of the movement of the planets. Take, for instance, the case of our earth, and let us discuss the consequences of the first law of motion. We know that the earth is moving each moment with a velocity of about eighteen miles a second, and the first law of motion assures us that if this globe were submitted to no external force, it would for ever pursue a straight track through the universe, nor would it depart from the precise velocity which it possesses at the present moment. But is the earth moving in this manner? Obviously not. We have already found that our globe is moving round the sun, and the comprehensive laws of Kepler have given to that motion the most perfect distinctness and precision. The consequence is irresistible. The earth cannot be free from external force. Some potent influence on our globe must be in ceaseless action. That influence, whatever it may be, constantly deflects the earth from the rectilinear path which it tends to pursue, and constrains it to trace out an ellipse instead of a straight line.

The great problem to be solved is now easily stated. There must be some external agent constantly influencing the earth. What is that agent, whence does it proceed, and to what laws is it submitted? Nor is the question confined to the earth. Mercury and Venus, Mars, Jupiter, and Saturn, unmistakably show that, as they are not moving in rectilinear paths, they must be exposed to some force. What is this force which guides the planets in their paths? Before the time of Newton this question might have been asked in vain. It was the splendid genius of Newton which supplied the answer, and thus revolutionised the whole of modern science.

The data from which the question is to be answered must be obtained from observation. We have here no problem which can be solved by mere mathematical meditation. Mathematics is no doubt a useful, indeed, an indispensable, instrument in the enquiry; but we must not attribute to mathematics a potency which it does not possess. In a case of this kind, all that mathematics can do is to interpret the results obtained by observation. The data from which Newton proceeded were the observed phenomena in the movement of the earth and the other planets. Those facts had found a succinct expression by the aid of Kepler's laws. It was, accordingly, the laws of Kepler which Newton took as the basis of his labours, and it was for the interpretation of Kepler's laws that Newton invoked the aid of that celebrated mathematical reasoning which he created.