Kepler's Third Law

Kepler’s Third Law says that objects orbiting the same central body move more slowly when their orbits are larger: if the semi-major axis increases, the period grows much faster because the orbital path is bigger and the orbital speed is lower. For bodies orbiting the same star or planet, the ratio T^2/a^3 stays constant, which comes from Newton’s version of gravity and the balance between gravitational pull and orbital motion. In the Solar System, this lets us compare or predict orbital periods using only the size of the orbit.

Use this law when comparing planets, moons, or satellites that orbit the same central mass, or when estimating an unknown orbital period from the orbit size. It is especially useful in astronomy and astrodynamics for circular and elliptical orbits around one dominant body.

• Using the formula for objects orbiting different central bodies without adjusting for the central mass
• Forgetting that a must be the semi-major axis, not the average distance or the closest approach
• Squaring or cubing the wrong quantity, such as writing T^3 ∝ a^2 instead of T^2 ∝ a^3