Satellites N and F have the same mass and are circular orbits about the same planet - AQA - A-Level Physics - Question 11 - 2019 - Paper 2
Question 11
Satellites N and F have the same mass and are circular orbits about the same planet. The orbital radius of F is greater than that of N.
Which is greater for F than ... show full transcript
Worked Solution & Example Answer:Satellites N and F have the same mass and are circular orbits about the same planet - AQA - A-Level Physics - Question 11 - 2019 - Paper 2
Step 1
A gravitational force on the satellite
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Answer
The gravitational force acting on a satellite in orbit can be expressed using the formula:
Fg=r2Gm1m2
Since both satellites have the same mass and are orbiting the same planet, the gravitational force will be greater for satellite N, which has a smaller orbital radius.
Step 2
B angular speed
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Answer
The angular speed ( \omega ) is given by ( \omega = \frac{v}{r} ) where ( v ) is the orbital speed. Since satellite F has a larger radius, its angular speed is lower than that of satellite N.
Step 3
C kinetic energy
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Answer
The kinetic energy (KE) of a satellite is given by:
KE=21mv2
In circular orbits, the orbital speed is related to the radius. Satellite F, with a larger radius, has a lower speed, resulting in lower kinetic energy compared to N.
Step 4
D orbital period
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The orbital period (T) can be calculated using Kepler's third law:
T=2πGMr3
As the orbital radius increases, the orbital period increases as well. Thus, the orbital period for F is greater than that for N.