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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

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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=GMmr2F = \frac{GMm}{r^2} 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=GMrv = \sqrt{\frac{GM}{r}} 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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The kinetic energy is given by KE=12mv2KE = \frac{1}{2}mv^2 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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The orbital period can be calculated using Kepler's third law: T=2πr3GMT = 2\pi\sqrt{\frac{r^3}{GM}} 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.

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