The three laws
Johannes Kepler's three laws of planetary motion form the foundation of classical orbital mechanics.
- Law of Orbits — Every planet moves on an elliptical path with the Sun at one focus.
- Law of Areas — The line joining a planet and the Sun sweeps out equal areas in equal times.
- Law of Periods — The square of the orbital period is proportional to the cube of the semi-major axis:
T² = (4π²/μ) · a³.
μ is the gravitational parameter (G·M). For Earth, μ = 398,600.4418 km³/s².
Why they matter
Kepler's third law lets you predict orbital period from altitude alone. An ISS-altitude orbit (~400 km) has a semi-major axis of ~6,778 km and a period of about 92 minutes. GEO sits at 42,164 km and takes exactly a sidereal day.
Intuition
- First law: orbits are not circles — circles are just a special case where eccentricity e = 0.
- Second law: spacecraft move fastest at periapsis and slowest at apoapsis. This is conservation of angular momentum.
- Third law: higher orbits are slower. Double the altitude and the period grows faster than linearly.
Test yourself below.