| 90 | The Solar System |
circle or an ellipse. Even if the nodes of the ellipse or its line of apsides regress or progress, this will only postpone the reëntrance of the curve into itself to the time when the nodes or perihelia, or both, shall have completed their revolutions.
No Permanent change in the axis.No permanent change in the inclination of the axis to the orbit can ever result from the pull of a second body upon the first's equatorial bulge.
Since action and reaction are equal and opposite, the equatorial protuberance is equally impotent to make the satellite travel permanently in its plane.
Same analytically.This appears also analytically in the expressions for the effect produced in the line of nodes and the effect upon the inclination, the former having in addition to its periodic terms a term which increases with the time, while the latter has no such term.
It may be worth pointing out here an error which has crept into Young's excellent text-books, in which he states that "Laplace and Tisserand have shown that the equatorial protuberance of a planet, due to its axial rotation, compels a near satellite to move nearly in the equatorial plane." Neither Laplace nor Tisserand has ever shown this or ever could.
Laplace and Tisserand.
