## Kepler’s Laws of Planetary Motion

08 Oct

1. The orbit of every planet is an ellipse with the sun at one of the two foci, which can be calculated with:

$r=\frac{p}{1+\varepsilon\, \cos\theta},$

2. A line joining a planet and the sun sweeps out equal areas during equal intervals of time. i.e. The planet has to move faster when it is closer to the sun.

3. The Square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The exact relation, which is the same for both elliptical and circular orbits, is given by the equation

$P^2 = \frac{4 \pi^2}{ G(M_1 + M_2)} a^3,$

for masses M1 and M2, and Newton’s gravitational constant G.