Page:Popular Astronomy - Airy - 1881.djvu/126

112 orbit, or the curvature of the path of a cannon ball, depends upon two circumstances; one is the velocity with which it is going, and the other is the force which acts in such a direction as to bend its path. The greater its speed, the less its path is curved; consequently, as the planet is going so exceedingly quick in the neighbourhood of K, its orbit may be very little curved there, even though the sun is there pulling it with a very great force. The effect of the planet's path being so little curved there, is, that the planet passes the sun and begins to recede from it. But it does not recede perpetually. Suppose, for instance, that it has reached the point M', and we examine the nature of the forces which act on it there. The force of the sun in the direction M'S may be resolved into two, in the directions N'M', O'M', of which the former only curves the orbit, while the latter retards the planet in its movement in the orbit. Therefore, as the planet recedes from the sun, it goes more and more slowly, till at last its velocity may be diminished so much, that the power of the sun, reduced as it is there, is enabled to bring it back again. That is the way the planet goes, revolving in its orbit, alternately approaching to, and receding from, the sun. Of course, in a series of lectures like these, I cannot go into every detail; but enough has been said to show that a planet when approaching the sun will not necessarily fall to the sun, and when receding from the sun will not recede beyond the hope of return. This is a stumbling-block to many a young astronomer who has not considered the subject well, but the remarks I have here made, will, on consideration, be found to be perfectly clear, and there is no doubt of their application.

From what I have shown, you will see that there