Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain, using momentum conservation, why a massive central body’s motion can be ignored, and estimate how small it is. (Guide: “The system: a massive body and a light satellite”; Practice Q7(c))
- I can explain why U_g is negative with the zero at infinity, and what a negative total energy means. (Guide: “Gravitational potential energy with the zero at infinity”)
- I can say which of E, L, K and U are constant in circular and in elliptical orbits, and justify each with a force or torque argument. (Guide: “What is conserved, and why”; Practice Q1)
- I can explain why a satellite moved to a higher circular orbit has more total energy but less kinetic energy. (Guide: Worked example 1; Practice Q5(d))
Calculation
- I can derive U_g = −GMm/r by integrating the gravitational force from infinity. (Guide: “Gravitational potential energy with the zero at infinity”)
- I can derive K = −½U and E = ½U = −GMm/(2r) for a circular orbit and use them. (Guide: “Energy in a circular orbit”; Practice Q2, Q5)
- I can predict how speed and energy change when a circular orbit’s radius changes by a given factor. (Practice Q3)
- I can use r_p v_p = r_a v_a with energy conservation to find unknown speeds or distances in an elliptical orbit. (Guide: Worked example 2; Practice Q6)
- I can derive v_esc = √(2GM/r), use it, and find the speed left over far away for a faster launch. (Guide: “Escape velocity”; Practice Q4)
Reasoning and graphs
- I can sketch K, U and E against r for circular orbits, with correct signs and shapes. (Guide: Figure 1; Practice Q5(c))
- I can use P = F · v to explain when gravity does work on a satellite and how its speed changes around an ellipse. (Practice Q7)
All ticked? You have finished Unit 6. Move on to Topic 7.1, Defining Simple Harmonic Motion, or return to the course roadmap.