Kepler's first law — ellipses

Statement

Each planet traces an ellipse with the Sun at one of its two foci. The Sun is not at the ellipse's center but offset toward a focus.

Why is it true?

An ellipse is described by two numbers: the semi-major axis a (size) and eccentricity e (flatness). With e = 0 it becomes a circle — the special case Copernic had assumed for all planets.

Earth's e ≈ 0.017 looks nearly circular, but Mars's e ≈ 0.093 and Mercury's e ≈ 0.21 were enough for Kepler to recognize in 1609 that the circle hypothesis was wrong — deduced from Tycho Brahe's observations.

Applications

Foundation for satellite orbit design, Hohmann transfer calculations between planets, models of exoplanet and binary-star orbits.

Topics that use this theorem

Related theorems

Step-by-step proofs