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Chapter 17 - SOLVING THE KEPLER PROBLEM

Published online by Cambridge University Press:  05 August 2013

Steven C. Frautschi ,
Richard P. Olenick ,
Tom M. Apostol  and
David L. Goodstein
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Summary

Therefore, during the whole time of their appearance, comets fall within the sphere of activity of the circumsolar force, and hence are acted upon by its impulse and therefore (by Corollary 1, Proposition XII) describe conic sections that have their foci in the center of the sun, and by radii drawn from the sun describe areas proportional to the times. For that force propagated to an immense distance, will govern the motions of bodies far beyond the orbit of Saturn.

Isaac Newton, Principia (1687)

SETTING THE STAGE

In 1543 Corpernicus published his famous book; a generation later Kepler formulated his three laws; and then 150 years after Copernicus's book, Isaac Newton took Kepler's third law and used it to deduce the law of universal gravitation. From the law of gravitation and his dynamics, Newton was able to deduce Kepler's other two laws.

The task of deducing all three of Kepler's laws from Newton's laws is called the Kepler problem. Its solution is one of the crowning achievements of Western thought.

It is part of our cultural heritage just as Beethoven's symphonies or Shakespeare's plays or the ceiling of the Sistine Chapel are part of our cultural heritage. But it differs from a symphony or a play or a painting in an important way. It is a living idea. It is not something to be executed or performed by others and merely admired by us.

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The Mechanical Universe
Mechanics and Heat, Advanced Edition
 , pp. 451 - 476
Publisher: Cambridge University Press
Print publication year: 1986

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