kepler_secnd_law

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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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K. Kepler's Second Law By studying the Danish astronomer Tycho Brahe's data about the motion of the planets, Kepler formulated three empirical laws; two of them can be stated as follows: Second Law A planet moves in a plane, and the radius vector (from the sun to the planet) sweeps out equal areas in equal times. First Law The planet's orbit in that plane is an ellipse, wi.th the sun at one focus. From these laws, Newton deduced that the force keeping the planets in their orbits had magnitude l/d2, where d was the distance to the sun; moreover, it was directed toward the sun, or as was said, central, since the sun was placed at the origin. Using a little vector analysis (without coordinates), this section is devoted to showing that the Second Law is equivalent to the force being central. It is harder to show that an elliptical orbit implies the magnitude of the force
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## This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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kepler_secnd_law - MIT OpenCourseWare http:/ocw.mit.edu...

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