Mechanism of the Heavens (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1831 Excerpt: ...and are therefore called Periodic Inequalities. 413. Thus the place of a planet, m, moving in its troubled orbit cdD, will be determined by the co-ordinates t; + Su, + 4#, r-f-Sr. These, however, are modified by a variation in the elements of the ellipse; for it is evident that, the path of the planet being clianged from -E to cD, the elements of the ellipse NwiE must vary. The variations of the elements are independent of the configuration or relative position of the bodies, and are only sensible in many revolutions; whereas those depending on the configuration, accomplish their changes in short periods. Thus v + St, s + Ss, r + Sr, may be regarded as the co-ordinates of the planet in its true orbit, provided the elements contained in these functions be considered to vary by very slow degrees. This perfectly accords with observation, whence it appears that the perihelia of the orbits of the planets and satellites have a very slow direct motion in space; that the nodes have a slow retrograde motion; and that the eccentricities and inclinations are perpetually varying by very slow degrees. These very slow changes are really periodic, but many ages elapse before they accomplish their revolutions;' on that account they are called Secular Inequalities, to distinguish them from the Periodic Inequalities, which pass rapidly from their maxima to their minima. Thus the Periodic Inequalities only depend on the configuration of the bodies, whereas the Secular Inequalities depend on the configuration of the perihelia and nodes alone. 414. La Grange took a new and very elegant view of the subject: --he considered the changes Su, $.-, Jr, to arise entirely from periodic and secular variations in the elements of elliptical motion, thus referring all the inequali...