Case study·Hard exam skill (4/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
A planet moves in the elliptical orbit shown. Its nearest distance from the Sun is at P and farthest distance is at A. The gravitational force is central, so angular momentum about the Sun is conserved.
Total: 5 marks
(a) Name the Kepler law connected with constant areal velocity. (1 mark)
(b) Write the angular-momentum relation between speeds at P and A. (1 mark)
(c) Find . (1 mark)
(d) If , find . (1 mark)
(e) State where the planet has greater kinetic energy. (1 mark)
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