Читать книгу The Circle of Knowledge: A Classified, Simplified, Visualized Book of Answers - Various - Страница 33

The laws under which the planets move were discovered through the genius of John Kepler, and are known as Kepler’s Laws of Planetary Motion. Kepler derived these laws from observation only, but Newton first explained them by showing that they were the necessary consequences of the laws of motion and the law of universal gravitation.

Kepler’s First Law states: “The earth and the other planets revolve in ellipses with the sun in one focus.”

Kepler’s Second Law states: “The radius vector of each planet moves over equal areas in equal times.”

Kepler’s Third Law states: “The squares of the periodic times of the planets are in proportion to the cubes of their mean distances from the sun.”

DIAGRAMS ILLUSTRATING KEPLER’S FIRST TWO LAWS OF PLANETARY MOTION

The diagram on the top illustrates the ellipse, and explains the first and second laws. The picture-diagram on the bottom illustrates the second law, which is that, as the planet moves round the sun, its radius vector describes equal areas in equal times. That is to say, a planet moves from A to B in the same time as it takes to move from C to D.

These laws cannot be fully understood without some acquaintance with mathematics. They may, however, be briefly explained for the comprehension of the non-mathematical reader. The figure in the diagram is an ellipse—what is known in popular language as an oval—which is symmetrical about the line AB, known as its major axis. It has two foci, S and S₁. The fundamental law of the ellipse is that if we take any point P on it, and join this point by a straight line to the two foci, then the sum of these two lines SP and S₁P is always the same—SP + S₁P = C.

The second law is rather less easy to understand. The radius vector is the line joining the sun to the planet at any moment; if we suppose the sun to be at the focus S, and P to be the planet, the radius vector at various positions of the planet will be represented by the lines SP, SP₁, SP₂, and so on. If the positions P, P₁, P₂, and so on, represent those which the planet occupies after equal periods of time—say, once a month—then the sectors of the ellipse bounded by each pair of lines, SP and SP₁, SP₁ and SP₂, will be equal. If a planet were to move in a circle round the sun, it is obvious that this law would imply that it moved with a uniform speed; but since the curvature of the ellipse varies in every part of its course, so must the speed of the planet, in order that its radius vector may describe equal areas in equal times. The planet will, in fact, be moving faster when it is near the sun, as at P, than when it is far off from the sun, as at P₂.

The third law shows that there is a definite numerical relation between the motions of all the planets, and that the time which each of them takes to complete its orbit depends upon its distance from the sun.

On his discovery of his third law Kepler had written: “The book is written to be read either now or by posterity—I care not which; it may well wait a century for a reader, as God has waited six thousand years for an observer.” Twelve years after his death, on Christmas Day, 1642, near Grantham, England, the predestined “reader” was born. The inner meaning of Kepler’s three laws was brought to light by Isaac Newton.