Question

Two satellites orbit the earth in circular orbits, each traveling at a constant speed. The radius of satellite A’s orbit is R, and the radius of satellite B’s orbit is 5R. Both satellites have the same mass. How does F_A, the centripetal force on satellite A, compare with F_B, the centripetal force on satellite B ?

• A. F_A = 25F_B
• B. F_A = 9F_B
• C. F_A = 20F_B
• D. F_A = 5F_B

Answer 1

The correct option is A F_A = 25F_B

Since the centripetal force on each satellite is equal to the gravitational force it feels due to the earth, the question is equivalent to, “How does F_A, the gravitational force on satellite A, compare to F_B, the gravitational force on satellite B?” Because both satellites have the same mass, Newton’s law of gravitation tells us that the gravitational force is inversely proportional to r². Since satellite B is 5 times farther from the center of the earth than satellite A, the gravitational force that satellite B feels is$\frac{1}{25}$ times the gravitational force felt by satellite A. (Be careful if you tried to apply the formula F_c =$\frac{m{v}^2}{r}$ for centripetal force and concluded that the answer was B. This is wrong because even though both satellites orbit at a constant speed, they don’t orbit at the same speed, so the formula for centripetal force cannot be used directly.)