Hegel and Newtonianism pp 415-427 | Cite as

# Universal Gravitation from Elliptical Orbits

## Abstract

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.

## Keywords

Direct Problem Elliptical Orbit Force Centre Conic Section Kepler Problem## Preview

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## Notes

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