Mathematical Theories of Planetary Motions (Classic Reprint)

The determination of the motions of the heavenly bodies is an important problem in and for itself, and also on account of the influence it has exerted on the development of mathematics. It has engaged the attention of the greatest mathematicians and in the course of their not altogether successful attempts to solve it, they have displayed unsurpassed ingenuity. The methods devised by them have proved useful not only in this problem but have also largely determined the course of advance in other branches of mathematics. Analytical mechanics, beginning with Newton and receiving a finished clearness from Lagrange, is especially indebted to this problem, and in turn, analytical mechanics has been so suggestive in method as to determine largely both the direction and rapidity of the advancement of mathematical science. Hence when it is desired to illustrate the abstract theories of analytical mechanics, the profundity of the mathematics of the problem of the motions of the heavenly bodies, its powerful influence on the historical development of this science, and flnally the dignity of its object, all point to it as most suitable for this purpose. This work ib intended not merely as an I introduction to the special study of astronomy, but rather for the student of mathematics who desires an insight into the creations of his masters in this field. The lack of a text-book, giving within moderate limits and in a strictly scientific manner the principles of mathematical astronomy in their present remarkably simple and lucid form, is undoubtedly the reason why so many mathematicians extend their knowledge of the solar system but little beyond Kepler slaws. The author has endeavored to meet this need and at the same time to produce a book which shall be so near the present state of the science as to include recent investigations and to indicate unsettled questions. The
(Typographical errors above are due to OCR software and don't occur in the book.)