The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance of A from the sun is greater than that of B from the sun? (a) 5 times (b) 2 times (c) 3 times (d) 6 times

Answer: (c). Kepler's third law: r ∝ T2/3. (rA)/(rB) = 82/3 = 4, so rA = 4rB. rA exceeds rB by 4rB - rB = 3rB. So the answer is (c) 3 times.

The period of revolution of planet A around the sun is 8 times that… | MHT CET 2021 (24 Sep, Shift 1)

Q17MHT CET 2021 · 24 SEP · SHIFT 1Easy

Kepler's Laws & Planetary Motion

The period of revolution of planet $\text{A}$ around the sun is 8 times that of planet $\text{B}$ . How many times the distance of A from the sun is greater than that of B from the sun?

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Answer: (c)

Kepler's third law: $r \propto T^{2/3}$ .
$\dfrac{r_A}{r_B} = 8^{2/3} = 4$ , so $r_A = 4r_B$ .
$r_A$ exceeds $r_B$ by $4r_B - r_B = 3r_B$ .
So the answer is (c) 3 times.

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