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Two satellites A and B (masses 200 kg and 400 kg) orbit the Earth at heights of 600 km and 1600 km respectively. If T_A and T_B are their orbital periods, find T_B - T_A. (Radius of Earth = 6400 km, mass of Earth = 6 x 10²⁴ kg.)

1. 1.33 x 10³ s
2. 3.33 x 10² s
3. 4.24 x 10³ s
4. 4.24 x 10² s

Correct answer: 1.33 x 10³ s

Solution

Orbital radii: r_A = 6400 + 600 = 7000 km = 7x10⁶ m, r_B = 6400 + 1600 = 8000 km = 8x10⁶ m. With GM = 6.67x10⁻¹¹ * 6x10²⁴ = 4.0x10¹⁴. T_A = 2*pi*sqrt((7x10⁶)³/4.0x10¹⁴) ~ 5.82x10³ s, T_B = 2*pi*sqrt((8x10⁶)³/4.0x10¹⁴) ~ 7.11x10³ s. Hence T_B - T_A ~ 1.29x10³ s ~ 1.33 x 10³ s.

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