Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 14 - Calculus of Vector-Valued Functions - 14.6 Planetary Motion According to Kepler and Newton - Preliminary Questions - Page 751: 3

Answer

If the semi-major axis $a$ is increased four-fold, then $T$ is increased by eight-fold.

Work Step by Step

Kepler's third law states that ${T^2}$ is proportional to ${a^3}$. It means that $T$ is proportional to ${a^{3/2}}$. If the semimajor axis $a$ is increased four-fold, then $T$ is increased by eight-fold.
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