Ellipsa

Meet Ellipsa, a planet tracing an ellipse with her star sitting at one focus.

Johannes Kepler, working from Tycho Brahe's careful observations of Mars, published in 1609 that planets move on ellipses with the Sun at one focus, not at the centre. Newton later showed that this follows from an inverse-square law of gravity. In polar form the orbit is r = a(1 − e²)/(1 + e cos θ), where θ is measured from the closest point, perihelion.

Earth's orbit has a ≈ 149.6 million km and e ≈ 0.0167. At perihelion, θ = 0, r = a(1 − e) ≈ 147.1 million km. At aphelion, θ = 180°, r = a(1 + e) ≈ 152.1 million km, a difference of about 5 million km.

The same equation describes comets on long, stretched orbits, satellites around Earth, and binary stars, and it is used to plan spacecraft trajectories.

Earth's seasons do not come from this distance change; we are closest to the Sun in early January. The sticker uses e = 0.6 to make the shape obvious. Real orbits also shift slowly because of other planets' pulls.