Answer
Result: See proof.
Work Step by Step
Since we have \[ r =\frac{k}{1 + e\cos(\theta)} \] where \(k > 0\). By assumption, \(r\) is minimal when \[ \cos(\theta) = 1 \Rightarrow \theta = 0, \] hence \(e \geq 0\). Result: See proof.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 12 - Vector-Valued Functions - 12.7 Kepler's Laws Of Planetary Motion - Exercises Set 12.7 - Page 902: 14
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