Escape Velocity & Energy of Orbits — A/L Physics

How do I practise Escape Velocity & Energy of Orbits?

1 question with a worked solution

1. What is the relationship between the escape velocity v_e from the surface of Earth (radius R, surface gravity g) and the orbital velocity v_o of a satellite in low Earth orbit skimming the surface?
   1. A) v_e = 2 · v_o
   2. B) v_e = 4 · v_o
   3. C) v_e = √2 · v_o
   4. D) v_e = v_o / √2
   Check my answer

   Correct answer: C) v_e = √2 · v_o

   Orbital velocity in low circular orbit is v_o = √(GM / R) = √(gR). Escape velocity from the surface is obtained by equating total mechanical energy to zero: ½ m v_e² - GMm/R = 0 => v_e = √(2GM / R) = √(2gR). Therefore, v_e = √2 · v_o ≈ 1.414 v_o.

   Show worked solution

   Step 1: v_o = √(GM / R) = √(gR). Step 2: v_e = √(2GM / R) = √(2gR). Step 3: v_e / v_o = √(2gR) / √(gR) = √2 => v_e = √2 · v_o. Answer: v_e = √2 · v_o.
   Modelled on: the A/L Physics examination pattern

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Where does Escape Velocity & Energy of Orbits fit in the syllabus?

Unit 5.5 · Year 1 · Term 3