We also saw that that elliptic orbit was produced according to Newton by the conjoint working of the centripetal and centrifugal forces in association with the three Laws of Motion, to which laws had to be added a corollary, which is termed the Parallelogram of Forces, before the First Law of Kepler could be fulfilled.
In making any hypothesis as to the physical cause of Kepler's Laws, if it can be shown that the same aetherial medium that gives rise to the centrifugal force, also gives rise to the centripetal force, and that the same medium by its rotatory motions also fulfils the three laws of motion, and gives a satisfactory physical explanation of all Kepler's Laws; then, according to our three Rules of Philosophy, we shall have found a physical medium which, by its motions and pressures and tensions, can give rise to all the phenomena exhibited in the celestial mechanism. Such a physical explanation will be philosophically correct, in that it is simple in its conception, is entirely in harmony with observation and experiment, and satisfactorily accounts for, and that on a physical basis, all the phenomena associated with the whole of the celestial mechanism.
We have therefore to apply the motions of the Aether medium to the solar system, and by so doing reveal the physical explanation of all Kepler's Laws, in the same way that Newton revealed their correctness from the mathematical standpoint. Let us review the conception of the solar system as given in [Art. 99], so that we may be able to proceed from that physical conception of a stationary solar system to a moving system.
Thus we see the sun in a stationary system occupying exactly the centre of that system. The solar energies are in full play, generating electro-magnetic Aether waves which are radiated forth into space with the velocity of light. Then, as there is given to the sun a rotatory motion on its axis, that rotatory motion imparts to the gravitating aetherial medium a circulatory or rotatory motion which spreads out through space with ever-increasing intensity.
By their radiating motion the Aether waves would repel all planets from their central body, the sun, if they were not counterbalanced by the centripetal force; and the two forces, the centrifugal and the centripetal forces, find their equilibrium at the mean distance of each planet, thus fixing and regulating permanently the distance and orbit of each planetary world.
At the same time, the rotatory motion of the electro-magnetic Aether currents, according to the second law of motion, would act on the planets by their kinetic or moving energy, and so circle them round the sun, their controlling centre. As long as the sun was quite stationary, while still possessing a rotation on its axis, if such a thing were possible, so long would the conception of the ancients be fulfilled, and the rotation of all the planets would be strictly circular in form, and their orbits would be that of a circle only, as proved by Sir W. R. Hamilton ([Art. 99]).
But, as is well known, the sun itself possesses an orbital motion of its own, so that, while all the associated planetary system is revolving round it, the sun with all that system is being carried along through space in an orbit which is also elliptic in form, as we shall see later on.
According to Herschel, the sun is moving towards the constellation of Hercules with a velocity of about 18,000 miles per hour, and the problem to be faced is, what is the effect of the sun's orbital velocity upon the circular motion of the planets? By solving that problem, we shall arrive at a physical conception for the first time of Kepler's Laws, and shall see that the first of Kepler's Laws is solved simply by giving an orbital velocity to any central body, the result of which will be that the circular form of any planet's orbit will be changed from the circular into one of elliptic form.
Let me ask the reader to perform a very simple experiment to confirm this fact. Take a piece of string and a lead pencil, and start to draw a circle on a piece of paper (Fig. 24). When, however, one quarter of the circle has been drawn, viz. D F, move the end of the piece of string representing the centre of the circle along the paper, as represented in the diagram, from A to B. The result will be that the pencil will now travel parallel with the moving centre for a time from F to G, and then, when the centre is brought to rest again, the other part of the half ellipse G H may be completed. In the same way, by reversing the motion, the other half of the ellipse may be completed. So that it is possible for an ellipse to be formed simply by moving the central point of a circle, and the motion of that central point will change the form of a circle into an ellipse. It is something like this that takes place in the planetary world, with this difference, that the central point which represents the sun does not return from one focus to another, but continues to journey on through space, with the result that the orbit of any planet is not strictly an ellipse, as we shall see later on. We have, then, the sun occupying the centre of the solar system, with all the planets revolving round it. We will take the sun and the Earth as examples. Let S in the diagram represent the sun, and E the Earth at its mean distance of 92,000,000 miles away (Fig. 25).