# Why do planets have elliptical orbits?

Feb 10, 2017

The works of Kepler and Newton proved that planets have elliptical orbits.

#### Explanation:

Johannes Kepler used observational data of Mars to derive his three laws of planetary motion. Kepler's first law states that a planet's orbit is an ellipse with the sun at one of the foci.

Later, Isaac Newton produced his laws of motion and gravity. By using Newton's laws and applying the conservation of energy and the conservation of angular momentum proves Kepler's first law.

The equation of the ellipse is:

$r = {r}_{0} / \left(1 + e \cos \theta\right)$

Where $r$ is the radial distance of the planet from the sun, $\theta$ is the angle the planets make from its perihelion, ${r}_{0}$ is the semi latus rectum distance and $e$ is the eccentricity of the ellipse.

Note that the orbit doesn't have to be an ellipse. If $e = 0$ the orbit is circular. If $e < 1$ the orbit is an ellipse. If $e = 1$ it is parabolic and if $e > 1$ it is hyperbolic. In both of these cases the planet gets ejected from the system. This does happen when the orbit gets perturbed by a large planet such as Jupiter.

In actual fact planetary orbits are only approximately elliptical. Orbits are constantly changing shape due to the gravitational influence of other planets.