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JEE Main 2022 (28 Jun, Shift 1) · Kepler's Laws & Planetary Motion

Kepler's Laws & Planetary Motion question from JEE Main 2022 (28 Jun, Shift 1)

Q11JEE Main 2022 · 28 JUN · SHIFT 1Easy

Kepler's Laws & Planetary Motion

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

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Answer: (c)

Kepler's third law: $\dfrac{r_A^3}{r_B^3} = \dfrac{T_A^2}{T_B^2}$ .
$T_A = 2T_B \Rightarrow \dfrac{r_A^3}{r_B^3} = 4$
So the answer is (c) $r_A^3 = 4r_B^3$ .

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