Dynamics of UCM

Ellipses and Kepler's First Law

(a) An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci ($f_1$ and $f_2$) is a constant. You can draw an ellipse as shown by putting a pin at each focus, and then placing a string around a pencil and the pins and tracing a line on paper. A circle is a special case of an ellipse in which the two foci coincide (thus any point on the circle is the same distance from the center). (b) For any closed gravitational orbit, $m$ follows an elliptical path with $M$ at one focus. Kepler's first law states this fact for planets orbiting the Sun.

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"OpenStax College, College Physics. January 28, 2013."

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Dynamics of UCM

Ellipses and Kepler's First Law

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