WACE Physics — Unit 3
Kepler's Laws — Flashcards & Quiz
Kepler's three laws describe the motion of planets and satellites and can be derived from Newton's law of universal gravitation applied to circular or elliptical orbits. WACE Physics Year 12 Unit 3 expects you to state and apply each law and to derive Kepler's third law (T² ∝ r³) from the condition that gravity provides centripetal force.
Key Points
- Kepler's First Law (Law of Ellipses): planets move in elliptical orbits with the Sun at one focus. Most planetary orbits are nearly circular.
- Kepler's Second Law (Law of Areas): a line joining a planet to the Sun sweeps out equal areas in equal times. Planets move faster when closer to the Sun.
- Kepler's Third Law (Law of Periods): T² ∝ r³, or T²/r³ = constant for all orbits around the same central body.
- Derivation: set gravity = centripetal force (GMm/r² = mv²/r) and substitute v = 2πr/T to get T² = (4π²/GM)r³.
- Applications: calculating satellite orbital periods, predicting orbital radii from period, analysing binary star systems.
- The constant in T²/r³ depends only on the mass of the central body (M) — the orbiting object's mass does not appear.
Common Mistakes to Avoid
- Applying Kepler's laws to orbits around different central bodies with the same constant — the constant depends on M.
- Forgetting the Second Law means planets move at non-uniform speed around elliptical orbits.
- Using diameter instead of radius in the Third Law.
- Mixing up astronomical units — Kepler's constant for the Solar System in SI units involves G and M_Sun.
- Treating all orbits as perfectly circular — in reality they are ellipses, but HSC/WACE often assumes circular.
Exam Strategy
SCSA Unit 3 Kepler questions give you period and radius data and ask you to apply the Third Law or derive it. Method: (1) state the law (T² ∝ r³ or T²/r³ = constant), (2) for calculations, set up the ratio T₁²/T₂² = r₁³/r₂³, (3) for derivations, set gravity equal to centripetal force. Use consistent units throughout.
Sample Flashcards
Q1: State Kepler's three laws.
1st: Planets orbit in ellipses with the Sun at one focus. 2nd: Equal areas swept in equal times. 3rd: T² ∝ r³ for bodies orbiting the same central mass.
Q2: How does Kepler's 2nd law relate to angular momentum conservation?
Gravity is radial (no torque), so L = mvr is conserved. When r decreases, v increases — producing equal-area sweeping.
Sample Quiz Questions
Q1: Kepler's first law says planets orbit in perfect circles.
Answer: FALSE
Orbits are ellipses with the Sun at one focus.
Q2: A planet moves faster when closer to the Sun.
Answer: TRUE
Equal areas in equal times requires greater speed at shorter radius.
Q3: T²/r³ is the same for objects orbiting different central bodies.
Answer: FALSE
The constant depends on the central body's mass M.
Revision Tip
Kepler's Third Law is the most tested — drill a Revizi deck with 8+ planetary or satellite problems using ratios and direct substitution.
Last updated: March 2026 · 2 flashcards · 3 quiz questions