The time period of X planet of our solar system is 8 years. The distance of earth from the sun is 1.5 × 10¹¹ m. The distance of the X planet from the sun will be: (a) 3√(2) × 10¹¹ m (b) 3 × 10¹¹ m (c) 6 × 10¹¹ m (d) 12 × 10¹¹ m

Answer: (c). Kepler's third law: rX = rE ((TX)/(TE))2/3. (8/1)2/3 = 4 rX = 4 × 1.5 × 10¹¹ = 6 × 10¹¹ m So the answer is (c) 6 × 10¹¹ m.

The time period of X planet of our solar system is 8 years. The… | JEE Main 2022 (30 Jul, Shift 2)

Q14JEE Main 2022 · 30 JUL · SHIFT 2Medium

Kepler's Laws & Planetary Motion

The time period of X planet of our solar system is $8$ years. The distance of earth from the sun is $1.5 \times 10^{11}\text{ m}$ . The distance of the X planet from the sun will be:

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Answer: (c)

Kepler's third law: $r_X = r_E \left(\frac{T_X}{T_E}\right)^{2/3}$ .
$\left(\frac{8}{1}\right)^{2/3} = 4$
$r_X = 4 \times 1.5 \times 10^{11} = 6 \times 10^{11}$ m
So the answer is (c) $6 \times 10^{11}\text{ m}$ .

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