# Planetary Motion (Kepler's Laws)

Kepler's laws describe the motion of planets around the sun and were published between 1609 and 1619 by Johannes Kepler.

**Kepler’s first law**

Every planet moves along an ellipse, with the sun located at a focus of the ellipse. To be more precise: sun and planets orbit their barycenter.

**Kepler’s second law**

An imaginary line joining any planet to the sun sweeps out equal areas in equal times. This law is illustrated in Figure 1. The time it takes a planet to move from position 1 to 2, sweeping out area 'A' is exactly the time taken to move from position 3 to 4, sweeping area 'B', these areas are the same, A=B. As can be shown, this law is a consequence of conversation of angular momentum.

**Kepler’s third law**

The square of the period of any planet is proportional to the cube of the semi-major axis of the orbit, ^{2} ~ a^{3}

**Figure 1:** Illustration of the first and second law. Note, that all planets, except Mercury, have nearly circular orbits and that the given illustration is highly exaggerated.