[Illustration: Fig. 46.—THE PLANE OF A PLANET’S ORBIT.]
We represent the movement in the adjoining figure. If A is started off with an initial velocity in the direction A T, the attraction of S will, however, make itself felt, even though A cannot move directly towards S. The body will not be allowed to travel along A T; it will be forced to swerve by the attraction of S; it will move from P to Q, gradually getting nearer to S. To enter into the details of the movement would require rather more calculation than it would be convenient to give here. Even though S is much more massive than A, we may suppose that the path which A follows is so great that the diameter of the globe S is quite insignificant in comparison with the diameter of the orbit which the smaller body describes. We shall thus regard both A and S as particles, and Kepler’s well-known law, to which we so often refer, tells us that A will revolve around S in that beautiful figure which the mathematician calls an ellipse. For our present purpose we are particularly to observe that the movement is restricted to a plane. The plane in which A moves depends entirely on the direction in which it was first started. The body will always continue to move in the same plane as that in which its motion originally commenced. This plane is determined by the point S and the straight line in which A was originally projected. It is essential for our argument to note that A will never swerve from its plane so long as there are not other forces in action beside those arising from the mutual attractions of A and S. The ordinary perturbations of one body by the action of others need not here concern us.
The case we have supposed will, of course, include that of the movement of a planet round the sun. The planet is small and represented by the body A, which revolves round the great body S, which stands for the sun. However the motion of the planet may actually have originated, it moves just as if it had received a certain initial impulse, in consequence of which it started into motion, and thus defined a certain plane, to which for all time its motion would be restricted.
So far we have spoken of only a single planet; let us now suppose that a second planet, B, is also to move in revolution about the same sun. This planet may be as great as A, or bigger, or smaller, but we shall still assume that both planets are inconsiderable in comparison with S. We may assume that B revolves at the same distance as A, or it may be nearer, or further. The orbit of B might also have been in the same plane as A, or—and here is the important point—it might have been in a plane inclined at any angle whatever to the orbit of A. The two planes might, indeed, have been perpendicular. No matter how varied may be the circumstances of the two planets, the sun would accept the control of each of them; each would be guided in its own orbit, whether that orbit be a circle, or whether it be an ellipse of any eccentricity whatever. So far as the attraction of the sun is concerned, each of these planets would remain for ever in the same plane as that in which it originally started. Let us now suppose a third planet to be added. Here again we may assume every variety in the conditions of mass and distance. We may also assume that the plane which contains the orbit of this third planet is inclined at any angle whatever to the planes of the preceding planets. In the same way we may add a fourth planet, and a fifth; and in order to parallel the actual circumstance of our solar system, so far as its more important members are concerned, we may add a sixth, and a seventh, and an eighth. The planes of these orbits are subjected to a single condition only. Each one of them passes through the centre of the sun. If this requirement is fulfilled, the planes may be in other respects as different as possible.