1.

Two satellites orbit the Earth in circular orbits, each travelling at a constant speed. The radius of satellite A's orbit is R, and the radius of satellite B's orbit is 3R. 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?

Answer»

`F_(A)=9F_(B)`
`F_(A)=3F_(B)`
`F_(A)=F_(B)`
`F_(B)=3F_(A)`

SOLUTION :Since the centripetal force on each satellite is equal to the gravitational force it feels due to the Earth, the QUESTION is equivalent no, "How does `F_(A)`, the gravitational force on satellite A, compare of `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 `r^(2)`. since satellite B is 3 times farther from the center of the Earth than satellite A, the gravitational force the satellite B feels is `((1)/(3))^(2)=(1)/(9)` the gravitational force felt by satellite A. (Be careful if you tried to apply the formula `F_(c)=(mv^(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.


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