If the distance of the earth from Sun is 1 . 5 × 10 6 km , then the distance of an imaginary planet from Sun, if its period of revolution is 2 . 83 years is:

Question

If the distance of the earth from Sun is 1 . 5 × 10 6 km , then the distance of an imaginary planet from Sun, if its period of revolution is 2 . 83 years is:, 6 × 10 7 km, 6 × 10 6 km, 3 × 10 6 km, 3 × 10 7 km

MARKS App · Accepted Answer

From Kepler's law of periods, we know that T 2 ∝ R 3 ⇒ T 1 T 2 2 = R 1 R 2 3 ⇒ 1 2 . 83 2 = 1 . 5 × 10 6 R 2 3 ⇒ R 2 = 2 . 83 2 × 1 . 5 × 10 6 3 1 3 = 8 1 3 × 1 . 5 × 10 6 = 3 × 10 6 km

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