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Two satellites S and S' orbit the Earth at distances 3R and 6R from its centre. What is the ratio of their orbital periods?

1. 1: 2
2. 2: 1
3. 1: 2¹.5
4. 1: 2⁰.67

Correct answer: 1: 2¹.5

Solution

By Kepler's third law T ∝ r^(3/2). The ratio T_S: T_S' = (3R)^(3/2): (6R)^(3/2) = (1/2)^(3/2): 1 = 1: 2^(3/2) = 1: 2¹.5.

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