How does eccentricity describe the shape of a planet's orbit?

In the context of the work of German astronomer Johannes Kepler, the eccentricity of a planet's orbit is a numerical measure of how much that orbit deviates from a perfect circle.12

Because planets travel in elliptical paths, eccentricity describes the degree of "flatness" of the ellipse. This relationship functions as follows:34

• Zero Eccentricity: An orbit with an eccentricity of 0 is a perfect circle.13
• Increasing Eccentricity: As the value increases toward 1, the ellipse becomes progressively more elongated or "flattened".32

Mathematically, eccentricity is determined by the ratio of the distance between the two focal points of the ellipse to the length of its major axis. While some planets, such as Earth, have orbits with very low eccentricity—making them nearly circular—others, like Mars, possess significantly more eccentric orbits. This variation means that a planet's distance from the Sun changes throughout its orbital period.213