Kepler's laws
Three empirical laws describing planetary orbits: (1) Planets move in elliptical orbits with the Sun at one focus. (2) A planet sweeps equal areas in equal times. (3) The square of a planet's orbital period is proportional to the cube of its semi-major axis: T² ∝ a³ or T²/a³ = constant.
Formula
T² ∝ a³ (T²/a³ = constant)
Real World
NASA used Kepler's third law to predict the orbital period of New Horizons' flyby trajectory around Pluto — confirming Pluto's orbital period of 248 years from its known distance of 39.5 AU from the Sun.
Exam Focus
For 'show that' questions on Kepler's third law, derive T²/r³ = 4π²/GM by equating gravitational force to centripetal force — don't just quote the formula.
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