Universal Gravitation from Elliptical Orbits

  • J. Bruce Brackenridge
Part of the Archives Internationales D’Histoire Des Idées / International Archives of the History of Ideas book series (ARCH, volume 136)


Of all the problems the Principia addresses, none is more important than the Kepler problem: the analysis of planetary motion, in which a body orbits in an ellipse under the action of an inverse square force directed toward a focus of the ellipse. The given for the contemporary physicist is that the force is an inverse square and the challenge for the student is to find the path that such a body will follow: that is, an ellipse. But the given for the seventeenth century physicist was the elliptical orbit and the challenge was to find the nature of the force: that is, the inverse square. The basic nature of this challenge is reflected in the seventeenth century terminology for the two problems: the force from the orbit is called the direct problem, and the orbit from the force is called the inverse problem. The primary challenge of Newon’s Principia is presented by the direct Kepler problem.


Direct Problem Elliptical Orbit Force Centre Conic Section Kepler Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • J. Bruce Brackenridge

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