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Question 16 of 36

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SAT Subject Test

A satellite moving in a circular orbit with respect to the Earth's center experiences a gravitational force. If the satellite is put into a new circular orbit of smaller radius, how will the gravitational force and the speed of the satellite change, if at all?

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Gravitational Force Speed
Decrease Decrease
Correct Answer: 
No
Gravitational Force Speed
Decrease Increase
Correct Answer: 
No
Gravitational Force Speed
Remain the same Remain the same
Correct Answer: 
No
Gravitational Force Speed
Increase Decrease
Correct Answer: 
No
Gravitational Force Speed
Increase Increase
Correct Answer: 
Yes

Both will increase. The gravitational force is proportional to l divided by r to the power of 2 end exponent, where r is the radius of the orbit. As the radius decreases the gravitational force increases. The centripetal force on the satellite is provided by the gravitational force and is proportional to the centripetal acceleration v to the power of 2 end exponent divided by r, where v is the speed. Therefore v to the power of 2 end exponent divided by r, is proportional to l divided by r to the power of 2 end exponent so v is proportional to l / r and also increases as the radius decreases.

Question Difficulty: 
medium