Satellites N and F have the same mass and move in circular orbits about the same planet - AQA - A-Level Physics - Question 13 - 2022 - Paper 2
Question 13
Satellites N and F have the same mass and move in circular orbits about the same planet. The orbital radius of N is less than that of F.
Which is smaller for N than... show full transcript
Worked Solution & Example Answer:Satellites N and F have the same mass and move in circular orbits about the same planet - AQA - A-Level Physics - Question 13 - 2022 - Paper 2
Step 1
A the gravitational force on the satellite
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Answer
The gravitational force, given by the formula
F=r2GMm
shows that as the radius (r) decreases, the force increases. Thus, N has a greater gravitational force than F.
Step 2
B the speed of the satellite
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Answer
The orbital speed is given by the equation
v=rGM
Since N is at a smaller radius, its speed will be higher than F's. Therefore, the speed is not smaller for N.
Step 3
C the kinetic energy of the satellite
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Answer
The kinetic energy is given by
KE=21mv2
Since the speed of N is greater, its kinetic energy will also be greater than that of F. Thus, this is not the correct answer.
Step 4
D the orbital period of the satellite
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Answer
The orbital period can be calculated using Kepler's third law:
T=2πGMr3
Since N has a smaller radius, it will have a smaller period because the period decreases with decreasing radius. Therefore, the orbital period is smaller for N than for F.