Orbital Motion & Satellites — A/L Physics

How do I practise Orbital Motion & Satellites?

1 question with a worked solution

1. A communications satellite moves in a stable circular orbit at radius r around Earth. If its orbital radius is increased to 4r, by what factor does its orbital period T change according to Kepler's Third Law?
   1. A) 8 times
   2. B) 4 times
   3. C) 2 times
   4. D) 16 times
   Check my answer

   Correct answer: A) 8 times

   According to Kepler's Third Law for circular orbits, T² ∝ r³ => T ∝ r^3/2. Increasing radius by a factor of 4 yields: T_new / T_old = (4)^3/2 = (√4)³ = 2³ = 8.

   Show worked solution

   Step 1: Kepler's third law: T² ∝ r³ => T ∝ r^3/2. Step 2: Substitute r_new = 4r: T_new / T_old = (4)^3/2 = (√4)³ = 8. Answer: 8 times.
   Modelled on: the A/L Physics examination pattern

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Where does Orbital Motion & Satellites fit in the syllabus?

Unit 5.4 · Year 1 · Term 3