Note N. 73 — SECTION III.

Note 73, p. 18. Motion of the nodes. Let S, fig. 19, be the sun; S N n the plane of the ecliptic; P the disturbing body; and p a planet moving in its orbit p n, of which p n is so small a part that it is represented as a straight line. The plane S n p of this orbit cuts the plane of the ecliptic in the straight line S n. Suppose the disturbing force begins to act on p, so as to draw the planet into the arc p pʹ; then, instead of moving in the orbit p n, it will tend to move in the orbit p pʹ nʹ, whose plane cuts the ecliptic in the straight line S nʹ. If the disturbing force acts again upon the body when at pʹ, so as to draw it into the arc pʹ pʺ, the planet will now 442tend to move in the orbit pʹ pʺ nʺ, whose plane cuts the ecliptic in the straight line S nʺ. The action of the disturbing force on the planet when at pʺ will bring the node to nʹʹʹ, and so on. In this manner the node goes backwards through the successive points n, nʹ, nʺ, nʹʹʹ, &c., and the line of nodes S n has a perpetual retrograde motion about S, the centre of the sun. The disturbing force has been represented as acting at intervals for the sake of illustration: in nature it is continuous, so that the motion of the node is continuous also; though it is sometimes rapid and sometimes slow, now retrograde and now direct; but, on the whole, the motion is slowly retrograde.