History of Western Philosophy - Bertrand Russell [300]
Kepler's great achievement was the discovery of his three laws of planetary motion. Two of these he published in 1609, and the third in 1619. His first law states: The planets describe elliptic orbits, of which the sun occupies one focus. His second law states: The line joining a planet to the sun sweeps out equal areas in equal times. His third law states: The square of the period of revolution of a planet is proportional to the cube of its average distance from the sun.
Something must be said in explanation of the importance of these laws.
The first two laws, in Kepler's time, could only be proved in the case of Mars; as regards the other planets, the observations were compatible with them, but not such as to establish them definitely. It was not long, however, before decisive confirmation was found.
The discovery of the first law, that the planets move in ellipses, required a greater effort of emancipation from tradition than a modern man can easily realize. The one thing upon which all astronomers, without exception, had been agreed, was that all celestial motions are circular, or compounded of circular motions. Where circles were found inadequate to explain planetary motions, epicycles were used. An epicycle is the curve traced by a point on a circle which rolls on another circle. For example: take a big wheel and fasten it flat on the ground; take a smaller wheel (also flat on the ground) which has a nail through it, and roll the smaller wheel round the big wheel, with the point of the nail touching the ground. Then the mark of the nail in the ground will trace out an epicycle. The orbit of the moon, in relation to the sun, is roughly of this kind: approximately, the earth describes a circle round the sun, and the moon meanwhile describes a circle round the earth. But this is only an approximation. As observation grew more exact, it was found that no system of epicycles would exactly fit the facts. Kepler's hypothesis, he found, was far more closely in accord with the recorded positions of Mars than was that of Ptolemy, or even that of Copernicus.
The substitution of ellipses for circles involved the abandonment of the æsthetic bias which had governed astronomy ever since Pythagoras. The circle was a perfect figure, and the celestial orbs were perfect bodies—originally gods, and even in Plato and Aristotle closely related to gods. It seemed obvious that a perfect body must move in a perfect figure. Moreover, since the heavenly bodies move freely, without being pushed or pulled, their motion must be 'natural'. Now it was easy to suppose that there is something 'natural' about a circle, but not about an ellipse. Thus many deep-seated prejudices had to be discarded before Kepler's first law could be accepted. No ancient, not even Aristarchus of Samos, had anticipated such an hypothesis.
The second law deals with the varying velocity of the planet at different points of its orbit. If S is the sun, and P1, P2 P3, P4 P5 are successive positions of the planet at equal intervals of time—say at intervals of a month—then Kepler's law states that the areas P1SP2, P2SP3, P3SP4, P4SP5 are all equal. The planet, therefore moves fastest when it is nearest to the sun, and slowest when it is farthest from it. This, again, was shocking; a planet ought to be too stately to hurry at one time and dawdle at another.
The third law was important because it compared the movements of different planets, whereas the first two laws dealt with the several planets singly. The third law says: If r is the average distance of a planet from the sun, and T is the length of its year, then r3 divided by T2 is the same for all the different planets. This law afforded the proof (as far as the solar system is concerned) of Newton's law of the inverse square for gravitation. But of this we shall speak later.
Galileo (1564–1642) is the greatest of the founders of modern science, with the possible exception of Newton. He was born on about the day on which Michelangelo died, and he died in the year in which Newton was born. I commend