Celestial Mechanics During the Two Decades 1957 - 1977

Abstract

Introduction N discovery of the law of gravitation and the laws of motion created the concept of dynamical systems and the field known today as celestial mechanics. (Astrodynamics, orbital mechanics, and space dynamics are recently introduced expressions, emphasizing the engineering aspects of celestial mechanics. This review will attempt to include pure and applied celestial mechanics.) Copernicus, Brahe, Kepler, Galileo, Newton, Euler, Laplace, Lagrange, Hamilton, Jacobi, Poincare, Hill, Birkhoff, Whittaker, Moulton, Brouwer, Clemence, Eckert, Herrick, Stumpff, and Chebotarev are some of the giants on whose shoulders we perch. This admittedly imcomplete list and its order are important. The first fourteen offered the background. The work of the last seven is included in the review, since they contributed directly to celestial mechanics in the past twenty years. Jhis review will concentrate on the results and problems in the past twenty years rather than on the names of the individual contributors, excepting the authors of major books. The preceding list also may aid the discussion of a criticism uttered so frequently by the ignorami: mechanics is a dead field since Newton 'solved all problems'. Has Kepler been asked why he is working on celestial mechanics when Copernicus all problems? And if Newton solved all what have the aforenamed giants and we done in the past 300 years? But let us move to Whittaker, who certainly all problems, in which case Moulton, Brouwer, Clemence, and Herrick have done nothing. If so, how may one report on advances in this field in the past 20 years? The answer is, of course, well known to the cognoscenti: celestial mechanics is alive and well and living at several centers. Significant contributions are being made and new problems are being solved daily, using techniques Newton never even dreamed about. Furthermore, new and challenging unsolved problems emerge continuously, assuring that celestial mechanics will continue to be an exciting field of research. What Is New in Celestial Mechanics?