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 for F? A. the gravitational force on the satellite B. the speed of the satellite C. the kinetic energy of the satellite D. the orbital period of the satellite

A-Level AQA Physics Orbits of Planets & Satellites: Satellites N and F have the same

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 acting on a satellite in orbit is given by the formula: $F = \frac{GMm}{r^2}$ where $G$ is the gravitational constant, $M$ is the mass of the planet, $m$ is the mass of the satellite, and $r$ is the distance (orbital radius) from the center of the planet. Since satellite N has a smaller radius ( $r_N < r_F$ ), the gravitational force on satellite N is actually greater than that on F. Thus, this option is incorrect.

Step 2

B. the speed of the satellite

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Answer

The speed of a satellite in a circular orbit is determined by the formula: $v = \sqrt{\frac{GM}{r}}$ Since satellite N has a smaller orbital radius than satellite F, its speed will be greater. This means the speed of the satellite N is not smaller than that of F. Therefore, this option is also incorrect.

Step 3

C. the kinetic energy of the satellite

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Answer

The kinetic energy (KE) of a satellite is given by: $KE = \frac{1}{2} mv^2$ Substituting the expression for speed into the kinetic energy formula, we find that the kinetic energy of satellite N, having a greater speed, will also be greater than that of satellite F. Hence, this option is also incorrect.

Step 4

D. the orbital period of the satellite

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Answer

The orbital period (T) of a satellite is given by: $T = 2\pi \sqrt{\frac{r^3}{GM}}$ Since satellite N has a smaller radius (r), its orbital period will also be less than that of F. Thus, this makes D the correct 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

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

A. the gravitational force on the satellite

B. the speed of the satellite

C. the kinetic energy of the satellite

D. the orbital period of the satellite

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