Two satellites A and B are revolving around a planet in coplanar and concentric circular orbits of radii R 1 and R 2 respectively in the same sense. Their respective periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of A is equal to 1 0 4 km . What is their relative speed when they are closest?

Step-by-step solution

By Kepler's third law T 2 ∝ R 3 or T 2 R 3 = constant ∴ T 1 2 T 2 2 = R 1 3 R 2 3 ∴ 1 64 = R 1 3 R 2 3 ∴ R 1 R 2 = 1 4 ∴ R 2 = 4 R 1 = 4 × 10 4   km Distance travelled by A in one revolution is S 1 = 2 π R 1 = 2 π × 10 4   km ∴ v 1 = S 1 T 1 = 2 π × 1 0 4 1 = 2 π × 1 0 4   km   h - 1 ∴ Similarly, v 2 = S 2 T 2 = 2 π × 4 × 1 0 4 8 = π × 1 0 4   km   h - 1 V 12 = V 1 − V 2