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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

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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=Gm1m2r2F_g = \frac{G m_1 m_2}{r^2} 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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The kinetic energy (KE) of a satellite is given by: KE=12mv2KE = \frac{1}{2}mv^2 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=2πr3GMT = 2\pi \sqrt{\frac{r^3}{GM}} As the orbital radius increases, the orbital period increases as well. Thus, the orbital period for F is greater than that for N.

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