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# Kepler's laws

Kepler's laws are principles of planetary (i.e. satellite) motion first recorded by Johannes Kepler (1571-1630).

Kepler's first law: The orbit of every planet is an ellipse with the primary at one of its foci (an ellipse can be thought of as an elongated circle with two "centres" or foci).

Kepler's second law: A line joining a planet to the sun sweeps out equal areas during equal intervals of time. The implication is that a planet goes much faster in the section of its orbit that is closer to the Sun.

Kepler's third law: The square of the orbital period $T$ is proportional to the cube of the semi major axis $a$ (one half of the longest diameter of the ellipse) of its orbit: $$T^2\propto a^3$$

The Sun is at a focus (f1) of the orbits of planet 1 and planet 2 (First Law). Planet 1 sweeps out section A1 and A2 (which are equal in area) implying a slower speed at A2. The semi-major axis is one half of the lines denoted a1 and a2 in the image (the longest axes of the ellipse).