An Introductory Treatise on the Lunar Theory
- ISBN-10
- 1230858679
- ISBN-13
- 9781230858678
- Category
- Lunar theory
- Pages
- 102
- Language
- English
- Published
- 2013-09
- Publisher
- Theclassics.Us
- Author
- Ernest William Brown
Description
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ...eliminated. The series of operations thus continually raises the order of the coefficients of the periodic terms in R. We go on with the operations until these coefficients become sufficiently small to be neglected. Delaunay has continued them until he has found all terms in the longitude correctly to the seventh order inclusive; in addition, some coefficients are calculated to higher orders when slow convergence indicated the necessity of carrying the approximations further. The number of operations required is very large. Delaunay retains all terms in R up to the eighth order inclusive. He first carries out 57 operations, by means of which he eliminates all periodic terms in R which are of an order less than the fourth. The first operation is that outlined in Art. 195 above; then follows the elimination of the terms with arguments 1, Ih + 2g + H-ih!-2tf-21' 1, etc.--those terms whose coefficients are lowered by the integrations being, in general, considered first. The expression for R (in which every term produced by the successive changes of the variables is shown separately) together with the details of these operations occupy the greater part of Vol. i.; the expression for R alone occupies pages 119-256. Vol. H. opens with the value of R which remains after the 57 operations have been carried out: it now contains no periodic term of an order less than the fourth and the great majority of the terms are of a higher order. He then makes 435 further operations in order to eliminate these remaining terms. In most of these operations it is not necessary to change the variables in R: the small changes produced are made in the coordinates only. There are, however, five periodic terms, arising from changes in R, to be taken into account...
