Eccentricity

How squashed is the conic? 0 = circle, <1 = ellipse, 1 = parabola, >1 = hyperbola.

Eccentricity measures how 'stretched' a conic section is.

Slide the eccentricity

ellipse

e = 0.50

e = 0 → circle · 0<e<1 → ellipse · e = 1 → parabola · e > 1 → hyperbola

Orbit lab — Kepler's laws in motion

Eccentricity e = 0.50

nearest the Sun 0.50·a

farthest 1.50·a

~3.0× faster at perihelion

The shaded wedge is the area swept by the radius in a fixed slice of time — it stays the same size all the way round (Kepler's 2nd law), so the planet must speed up when it's close to the Sun and crawl when it's far. e = 0 ⇒ a circle; bigger e ⇒ a more stretched ellipse with the Sun further off-centre.

By value

e = 0 — circle.
0 < e < 1 — ellipse.
e = 1 — parabola.
e > 1 — hyperbola.