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On the Geometry of the Kepler Problem

by John Milnor

Year of Award: 1984

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 90, 1983, pp. 353-365

Summary: This paper defines a Kepler orbit as any curve in three-space that is a solution to the Newtonian two-body problem.  The paper then shows that a particular manfold can be identified with one of the three classical geometries (Euclidean, spherical, or Lobachevskian) so that each "straight line" in this geometry corresponds to a unique Kepler orbit.

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About the Author: (from The American Mathematical Monthly, vol. 90, (1983)) John Milnor received his Ph.D. at Princeton University in 1954, under the direction of Ralph Fox. As a student, he was also strongly influenced by Norman Steenrod, and by a year in Zürich under Heinz Hopf. After teaching for some years at Princeton University, interrupted by stays in Oxford, Berkeley, U.C.L.A., and M.I.T., he moved across town to the Institute for Advanced Study. His mathematical work was centered around the topology of manifolds and related areas of algebra.


Subject classification(s): Geometry and Topology | Analytic Geometry | Index
Publication Date: 
Wednesday, September 24, 2008