Aether and Gravitation

by William George Hooper

By the time the planet has arrived at point C, its motion through space has gradually decreased, and the Centripetal Force begins to re-assert itself, with the result that the earth is slowly made to proceed towards the point D of the ellipse, at which point its motion is the slowest in orbital velocity, only travelling about 16 miles per second, while the distance of the earth from the sun is the greatest and has increased from 91,000,000 miles at the perihelion to 94,500,000. This point of the orbit is known as its aphelion.

After rounding this point, the orbital velocity of the earth begins to increase again, owing to the diminishing distance of the earth from the sun, which according to the law of inverse squares ([Art. 22]) gives an added intensity to the Centripetal Force.

Thus by the combination of the Laws of Motion and the Law of Gravitation discovered by Newton, he was able to satisfactorily account for and explain on a mathematical basis, the reason why the earth and all the other planets move round the sun in elliptic orbits, according to Kepler's First Law.

In the development of the physical cause of gravitation, therefore, the same physical medium, which accounts for that law, must also give a satisfactory explanation of the first of Kepler's Laws.

Art. 27. Kepler's Second Law.--This law states that the Radius Vector describes equal areas in equal times. The Radius Vector is the imaginary straight line joining the centres of the sun and the earth or planet. While the First Law shows us the kind of path which a planet takes in revolving round the sun, the Second Law describes how the velocity of the planet varies in different parts of its orbit.

If the earth's orbit were a circle, it can be readily seen that equal areas would be traversed in equal times, as the distance from the sun would always be the same, so that the Radius Vector being of uniform length, the rate of motion would be uniform, and consequently equal areas would be traversed in equal times. Take as an illustration the earth, which describes its revolution round the sun in 365-1/4 days. Now if the orbit of the earth were circular, then equal parts of the earth's orbit would be traversed by the Radius Vector in equal times. So that with a perfectly circular orbit, one half of the orbit would be traversed by the Radius Vector in half a year, one quarter in one quarter of a year, one-eighth in one-eighth of a year, and so on; the area covered by the Radius Vector being always exactly proportionate to the time.

From Kepler's First Law, however, we know that the planet's distance does vary from the sun, and therefore the Radius Vector is sometimes longer and sometimes shorter than when the earth is at its mean distance; the Radius Vector being shortest at the perihelion of the orbit, and longest at the aphelion. We learn from Kepler's Second Law that when the Radius Vector is shortest, that is, when the planet is nearest the sun, it acquires its greatest orbital velocity; and when the Radius Vector is longest, that is, when the planet is farthest from the sun, the orbital velocity of a planet is the slowest.

Let A, B, D, C represent the elliptic orbit of a planet, with S sun at one of the Foci, and let the triangles A, S, B and D, S, C be triangles of equal area. Then, according to Kepler's Second Law, the time taken for the Radius Vector to traverse the area A, S, B is equal to the time that the Radius Vector takes to traverse the area D, S, C. So that the planet would take an equal time in going from A to B of its orbit, as it would take in going from D to C. Thus the nearer the planet is to the sun, the greater is its orbital velocity, and the farther it is away from the sun the slower is its velocity, the velocity being regulated by the distance. The manner in which the difference of velocity is accounted for by the Law of Gravitation has already been explained in the preceding article. Thus Newton proved that Kepler's Second Law was capable of being mathematically explained, and accounted for, by the universal Law of Gravitation.

If, therefore, a physical cause can be given for Newton's Law of Gravitation, then such physical cause must also be able to account for, and that on a strictly philosophical basis, the second of Kepler's Laws as well as the first.