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Question 33 of 36

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SAT Subject Test

The Earth has a radius of 6 comma 400 kilometers. A satellite orbits the Earth at a distance of 12 comma 800kilometers from the center of the Earth. If the weight of the satellite on Earth is 100 kilonewtons, the gravitational force on the satellite in orbit is

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11 kilonewtons

Correct Answer: 
No

25 kilonewtons

Correct Answer: 
Yes

50 kilonewtons

Correct Answer: 
No

100 kilonewtons

Correct Answer: 
No

200 kilonewtons

Correct Answer: 
No

The correct answer is 25 kilonewtons. The weight of the satellite on Earth is the same as the gravitational force on it, and the gravitational force F on an object due to Earth is inversely proportional to the square of the distance r of the object from the center of Earth left parenthesis F proportional to 1 over r squared right parenthesis. In the given orbit, the satellite is twice as far from the center of Earth than when it is on Earth’s surface, so the gravitational force on it is one fourth as great. Therefore the gravitational force on the satellite in orbit is 100 kilonewtons divided by 4, which is equal to 25 kilonewtons.

Question Difficulty: 
hard