orbital period hard

Question

A satellite shifted from radius r to 4r. New period compared to old T is:

RankGuru · Accepted Answer

From Kepler's 3rd Law: $T \propto r^{3/2}$.
Given $r' = 4r$:
$T' = T 	imes (4)^{3/2} = T 	imes (\sqrt{4})^3 = T 	imes (2)^3 = 8T$.

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