A planet's semi-major axis is doubled. Its orbital period changes by a factor of approximately:
A$2$, since $T \propto r$ in the simple case here
B$4$, since $T \propto r^2$ for circular planets
C$2\sqrt{2}$, since $T \propto r^{3/2}$ by Kepler
D$8$, since $T^3 \propto r^2$ on the chart
Answer & Solution
Correct answer: C. $2\sqrt{2}$, since $T \propto r^{3/2}$ by Kepler
$T^2 \propto r^3$ so $T \propto r^{3/2}$; doubling $r$ gives factor $2^{3/2} = 2\sqrt 2$.
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