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 Newton’s third law and the ratio m/M, why a massive central body can be treated as fixed. (Guide: “A two-object system”; Practice Q4)
- I can explain why a satellite’s angular momentum about the central body is constant in any orbit. (Guide: “Two conservation laws constrain every orbit”; Practice Q6)
- I can state which quantities are constant in a circular orbit and which change in an elliptical orbit. (Guide: “Circular orbits” and “Elliptical orbits”; Practice Q1, Q2)
- I can explain why U_g = −GMm/r is negative and what the sign of E says about whether a satellite is bound. (Guide: “Zero at infinity: bound and unbound”; Practice Q6)
Calculation
- I can derive K = GMm/(2r) and E = −GMm/(2r) for a circular orbit and use them. (Guide: Worked example 1; Practice Q4)
- I can find the energy needed to move a satellite between circular orbits. (Guide: Worked example 1; Practice Q4)
- I can use v_near r_near = v_far r_far and energy conservation on an elliptical orbit. (Guide: Worked example 2; Practice Q6)
- I can derive v_esc = √(2GM/r) and find how far a slower probe rises, or how fast a faster one moves far away. (Guide: Worked example 3; Practice Q3, Q7)
Reasoning and skills
- I can sketch how K, U_g and E depend on orbital radius, and linearise orbit data by plotting E against 1/r. (Guide: Figure 1; Practice Q5)
- I can explain, in terms of the work done by gravity, why a satellite slows down as it moves away. (Guide: “Elliptical orbits”; Practice Q6)
- I can argue that escape speed does not depend on the satellite’s mass. (Guide: “Escape speed”; Practice Q7)
- I can explain why mgh fails for large changes in distance and use −GMm/r instead. (Guide: Worked example 3; Practice Q7)
All ticked? Move on to Topic 7.1, Defining Simple Harmonic Motion, or return to the course roadmap.