Kepler's three laws describe the shape, changing speed, and orbital period of planets moving around the Sun. They are part of D.1 Gravitational fields for both SL and HL.
The Three Laws
| Law | Statement | Physical meaning |
|---|---|---|
| First law | Each planet follows an elliptical orbit, with the Sun at one focus of the ellipse. | The Sun is not generally at the centre of the orbit. A circular orbit is the special case in which the two foci coincide. |
| Second law | A line joining a planet to the Sun sweeps out equal areas in equal time intervals. | The planet moves faster when it is closer to the Sun and slower when it is farther away. |
| Third law | The square of the orbital period is proportional to the cube of the orbit's semi-major axis: . | For bodies orbiting the same central mass, is constant. |
Why the Laws Work
Kepler developed these laws from astronomical observations. Newton later explained them using universal gravitation and the laws of motion.
For a circular orbit of radius , gravitational force provides the centripetal force:
Using gives
This is the circular-orbit form of Kepler's third law. For an elliptical orbit, is replaced by the semi-major axis . The proportionality constant depends on the central mass , so the same value applies only when the orbiting bodies share the same central body.
A common misconception is that a planet moves at constant speed throughout an elliptical orbit. It does not: Kepler's second law requires its speed to increase near the Sun and decrease farther away.
Exam Technique
For an IB State question, give all three laws precisely. In calculations, use only for bodies orbiting the same central mass, and distinguish the semi-major axis from the planet's instantaneous distance from the Sun.