Kepler's first law

Beginner

Planets orbit the Sun in ellipses with the Sun at a focus.

Key relationorbit

Planets move on ellipses with the Sun at one focus. Circles are special cases. Newton showed this comes from an inverse-square force.

Worked example

Earth's orbit eccentricity 0.017 is almost circular.

Common mistake

The Sun is at a focus, not the centre.

In more detail

Kepler's first law states that planets move in ellipses with the Sun at one focus. Newton's gravity explains this result.

Astronomers predict planetary positions using elliptical orbits.
Comet orbits are described as ellipses, often very elongated.
Astronomers use the elliptical shape of planetary orbits to predict where a planet will be at a given time.

Are orbits always ellipses?

For two-body gravity, yes, including circles as special cases.

Who discovered this law?

Johannes Kepler, from observations of Mars by Tycho Brahe.

Are all orbits ellipses?

Planetary orbits are ellipses to a good approximation, and circles are a special case with zero eccentricity.