Aether and Gravitation

by William George Hooper

It has also been found that certain comets have orbits which cannot be distinguished from that of an elongated ellipse, the sun occupying one of the Foci.

Now let us apply the Law of Gravitation to Kepler's First Law, and note carefully its application.

Let A, B, C, D be an ellipse representing the orbit of the earth, and let S represent the sun situated at one of the Foci.

We will suppose that the earth is projected into space at the point A, then according to the First Law of Motion, it would proceed in a straight line in the direction of A E, if there were no other force acting upon the earth. But it is acted upon by the attraction of the sun, that is the Centripetal Force which is exerted along the straight line S A ([Art. 20]), which continues to act upon it according to the principle already explained in [Arts. 21] and [22].

Now, according to the Second Law of Motion and the Parallelogram of Forces, instead of the earth going off at a tangent in the direction of A E, it will take a mean path in the direction of A B, its path being curved instead of being a straight line.

If the sun were stationary in space, then the mean distance, that is, the length of the imaginary straight line joining the sun S A to the earth, would remain unaltered. The Radius Vector S A, or the straight line referred to, would then be perpendicular to the tangent, and the velocity of the earth round the sun would be uniform, its path being that of a circle.

The Radius Vector S A, however, is not always perpendicular to the tangent F E, and therefore the velocity of the earth is not always uniform in its motion in its orbit, as sometimes it travels at a lesser or greater speed than its average speed, which is about 18 miles per second.

It has to be remembered that the sun itself is in motion, having a velocity through space of about 4-1/2 miles per second, so that, while the earth is travelling from A to B the sun is also travelling in the direction of S B. Thus the orbital velocity of the earth, and the orbital velocity of the sun, together with the Centripetal Force or universal Gravitation Attraction, are all acting in the same direction when the earth is travelling from A to B, that is, in the direction of the orbit situated at B. This point of the orbit is known as the perihelion, and at that point the velocity of the earth is at its greatest, because the earth is then nearest the sun.

According to Newton, the planet when at B would still have a tendency to fly off into space owing to its Centrifugal Force, but it is held in check by the Centripetal Force, so that instead of it flying off into space, it is whirled round and starts off on its journey away from the sun in the direction of B, C. The sun, however, is still continuing its journey in the direction of S, H, so that not only is the increased orbital velocity of the earth, which it obtained at its perihelion, urging the earth away from the sun, but the sun itself in its advance through space is leaving the earth behind it. The combined effect of the two motions, the advancing motion of the sun, and the receding motion of the earth, due to its increased orbital velocity, drives the earth towards the aphelion, where its distance from the sun is greatest, and its orbital velocity is the least.