CHAPTER XIII - THEORY OF THE AXES, PERIHELIA, AND EXCENTRICITIES

Summary

(652.) In the foregoing chapter we have sufficiently explained the action of the orthogonal component of the disturbing force, and traced it to its results in a continual displacement of the plane of the disturbed orbit, in virtue of which the nodes of that plane alternately advance and recede upon the plane of the disturbing body's orbit, with a general preponderance on the side of advance, so as after the lapse of a long period to cause the nodes to make a complete revolution and come round to their former situation. At the same time the inclination of the plane of the disturbed motion continually changes, alternately increasing and diminishing; the increase and diminution however compensating each other, nearly in single revolutions of the disturbed and disturbing bodies, more exactly in many, and with perfect accuracy in long periods, such as those of a complete revolution of the nodes and apsides. In the present and following chapters we shall endeavour to trace the effects of the other components of the disturbing force,—those which act in the plane (for the time being) of the disturbed orbit, and which tend to derange the elliptic form of the orbit, and the laws of elliptic motion in that plane. The small inclination, generally speaking, of the orbits of the planets and satellites to each other, permits us to separate these effects in theory one from the other, and thereby greatly to simplify their consideration. Accordingly, in what follows, we shall throughout neglect the mutual inclination of the orbits of the disturbed and disturbing bodies, and regard all the forces as acting and all the motions as performed in one plane.