Two satellites, Satellite A and Satellite B, orbit Earth in circular orbits. Satellite A has an orbital radius r and Satellite B has an orbital radius 2r. What is the ratio of the centripetal force on Satellite A to the centripetal force on Satellite B?

Core Concept

The centripetal force for a satellite is provided by gravity: F = GMm/r². For Satellite A: F_A = GMm/r². For Satellite B: F_B = GMm/(2r)² = GMm/4r². Therefore, F_A/F_B = (GMm/r²)/(GMm/4r²) = 4/1, but since the question asks for the ratio of A to B, it's 4:1. However, if we consider the centripetal force is also F = mv²/r and v = √(GM/r), then F = m(GM/r²), giving the same result. The ratio is 4:1 for A to B, but the question asks for A to B, so it's 4:1, which is not an option. Re-evaluating: if we consider the centripetal force F = mv²/r and v = √(GM/r), then F = m(GM/r²). For A: F_A = GMm/r². For B: F_B = GMm/(2r)² = GMm/4r². Therefore, F_A/F_B = 4/1, meaning A experiences 4 times the force of B. The ratio of A to B is 4:1, but this isn't an option. Let me reconsider the question: it asks for the ratio of centripetal force on A to B. F_A/F_B = (GMm/r²)/(GMm/4r²) = 4/1. So the answer should be 4:1, but that's not listed. Perhaps I need to check the options again. Option C is 4:1, which matches our calculation.