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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?
Select an Answer
| 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
View Correct Answer
Both will increase. The gravitational force is proportional to 
, where 
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 
, where 
is the speed. Therefore , is proportional to so is proportional to and also increases as the radius decreases.
Question Difficulty:
medium