Solved: Planetary Motion The planets travel in elliptical orbits with the sun as a

Chapter 10, Problem 62

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Planetary Motion The planets travel in elliptical orbits with the sun as a focus, as shown in the figure.

(a) Show that the polar equation of the orbit is given by

\(r=\frac{\left(1-e^{2}\right) a}{1-e \cos \theta}\)

where e is the eccentricity.

(b) Show that the minimum distance (perihelion) from the sun to the planet is r = a(1 - e) and the maximum distance (aphelion) is r = a(1 + e)

Text Transcription:

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r = (1 - e^2}) a / 1 - e cos theta