Aether and Gravitation. William George Hooper
theory must be reconstructed in order that our philosophy may be made to agree with our experiments and our experience.
[1]Lectures on Scientific Subjects.
Art. 25. Kepler's Laws.--A long time before Newton had discovered the Law of Gravitation, Kepler had found out that the motions of the planets were governed by certain laws, and these came to be known as Kepler's Laws.
These laws which were given to the world by Kepler, simply represented facts or phenomena which had been discovered by observation, as Kepler was unable to account for them, or to give any mathematical basis for the same.
On the discovery, however, of Universal Gravitation, Newton saw at once that these laws were simply the outcome of the application of the Law of Gravitation to the planets, and that they could be accounted for on a mathematical basis by the Law of Gravitation, as they seemed to flow naturally from that law.
Kepler's Laws are three in number and may be thus stated--
1st Law. Each planet revolves round the sun in an elliptic orbit, with the sun occupying one of the Foci.
2nd Law. In the revolution of a planet round the sun, the Radius Vector describes equal areas in equal times.
3rd Law. The squares of the periodic times of planets are proportional to the cubes of their mean distances.
Now the question arises, whether it is possible to form a theory of the Aether which shall satisfactorily and philosophically account for all the phenomena associated with Kepler's Laws in their relation to the motions of planets, satellites, or other solar bodies? On the present conception of the Aether such a result is an absolute impossibility. With the theory of the Aether, however, to be submitted to the reader in this work, the result is possible and attainable. If, therefore, such a result is philosophically proved, as I submit will be done, then we shall have greater evidence still that the theory so propounded is a more perfect theory than the one at present recognized by scientists generally.
Art. 26. Kepler's First Law.--Each planet revolves round the sun in an elliptic orbit, the sun occupying one of the Foci.
The ancients thought that the paths of the planets around the sun were circular in form, because they held that circular motion was perfect. A system of circular orbits for the paths of the planets round the sun would be very simple in its conception, and would be full of beauty and harmony. But exact calculations reveal to us that the path of a planet is not exactly that of a circle, as the distance of a planet from the sun in various parts of its orbit is sometimes greater, and sometimes less, than its mean distance.
The planet Venus has the nearest approach to a circular orbit, as there are only 500,000 miles between the mean, and greatest and least distances, but both Mercury and Mars show great differences between their greatest and least distances from the sun.
If, therefore, the orbits of a planet are not exactly circular, what is their exact shape? Kepler solved this problem, and proved that the exact path of a planet round its central body the sun was that of an ellipse, or an elongated circle. Thus he gave to the world the first of his famous laws which stated that each planet revolves round the sun in an orbit which has an elliptic form, the sun occupying one of the Foci.
Not only is the orbit of a planet round the sun elliptic in form, but the path of the moon round the earth, or the path of any satellite, as for example a satellite of Mars or Jupiter or Saturn, is also that of an ellipse, the planet round which it revolves occupying one of the Foci.
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 4–½ 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.
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