Definition
Eccentricity, written e, is one of the six Keplerian elements of an orbit. It tells how far the orbit departs from a circle, independently of its size. For an ellipse it is the distance from the centre to a focus, c, divided by the semi-major axis a: e = c / a. The Sun sits at one focus, so e is also the fraction of a by which the Sun is off-centre.
The same number classifies every conic section a body can follow under gravity. A closed orbit has e < 1; an object with e ≥ 1 passes the Sun once and never comes back.
| Value of e | Shape | Example |
|---|---|---|
| e = 0 | Circle | An idealised orbit; Venus comes close (0.007) |
| 0 < e < 1 | Ellipse | All planets, most asteroids, periodic comets |
| e = 1 | Parabola | The boundary between bound and unbound orbits |
| e > 1 | Hyperbola | Interstellar objects such as 1I/ʻOumuamua |
From a and e to the shape of the orbit
With the semi-major axis a and the eccentricity e, every other dimension of the ellipse follows:
perihelion distance q = a (1 − e)aphelion distance Q = a (1 + e)semi-minor axis b = a √(1 − e²)e = (Q − q) / (Q + q)Example for Mars, with a = 1.5237 AU and e = 0.0934: q = 1.381 AU (206.6 million km) and Q = 1.666 AU (249.2 million km). The distance to the Sun swings by 42 million km, and the sunlight Mars receives varies by (Q/q)² = 1.45, that is 45 %.
The last relation is handy in practice: measure the closest and farthest distances of a comet or a probe, and the eccentricity follows directly.
Eccentricities in the solar system
| Body | e | Perihelion | Aphelion |
|---|---|---|---|
| Mercury | 0.2056 | 0.307 AU | 0.467 AU |
| Venus | 0.0068 | 0.718 AU | 0.728 AU |
| Earth | 0.0167 | 0.983 AU | 1.017 AU |
| Mars | 0.0934 | 1.381 AU | 1.666 AU |
| Jupiter | 0.0484 | 4.95 AU | 5.46 AU |
| Saturn | 0.0539 | 9.02 AU | 10.05 AU |
| Uranus | 0.0473 | 18.3 AU | 20.1 AU |
| Neptune | 0.0086 | 29.8 AU | 30.3 AU |
| Pluto | 0.249 | 29.7 AU | 49.3 AU |
| Halley's comet | 0.967 | 0.59 AU | 35 AU |
Pluto's eccentricity is large enough that, between 1979 and 1999, it was closer to the Sun than Neptune. The two never collide because Pluto is locked in a 3:2 resonance with Neptune and is always far from it when it crosses Neptune's distance.
Why Earth's orbit looks like a circle
An eccentricity of 0.0167 does not mean a visibly squashed ellipse. The semi-minor axis is b = a √(1 − e²) = 0.99986 a: drawn with a = 10 cm, the ellipse is narrower than the circle by 0.014 mm, far thinner than a pencil line. What eccentricity really does is move the Sun off-centre: c = a e is about 2.5 million km for the Earth, so the Earth-Sun distance ranges from 147.1 million km in early January to 152.1 million km in early July.
The effect on sunlight is a 6.9 % difference between perihelion and aphelion, smaller than the effect of the axial tilt, which is why it is winter in the northern hemisphere when the Earth is closest to the Sun. In the heliocentric view, the orbits of Venus, the Earth and Neptune look like circles, while those of Mercury, Mars and Pluto are visibly off-centre around the Sun.
Eccentricity in the computations
To place a planet on its orbit, Meeus solves Kepler's equation, E − e sin E = M, which links the mean anomaly M (growing uniformly with time) to the eccentric anomaly E. The larger e, the more iterations are needed; for e close to 1 the classical iteration converges badly and Astronomical Algorithms gives dedicated methods for near-parabolic orbits.
For small eccentricities the difference between the true and the mean anomaly, the equation of the centre, can be written as a series:
C ≈ 2e sin M + (5/4) e² sin 2M + …For the Earth, C reaches about 1.9°: this is why the Sun moves faster along the ecliptic in January than in July, and why the March-to-September half of the year is about a week longer than the September-to-March half. It is also one of the two causes of the equation of time.
Eccentricities change
Eccentricity is not fixed. The pull of the other planets makes it oscillate slowly: the Earth's eccentricity varies between almost zero and about 0.06, with main periods of roughly 100,000 and 405,000 years, and is currently decreasing. These variations are one of the Milankovitch cycles that pace the ice ages.
Objects coming from outside the solar system have e > 1 by a large margin: 1I/ʻOumuamua (2017) had e ≈ 1.20, 2I/Borisov (2019) e ≈ 3.36, and 3I/ATLAS (2025) about 6, the most hyperbolic orbit ever measured.
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Frequently asked questions
What is Earth's orbital eccentricity?
About 0.0167. The Earth-Sun distance varies between 147.1 million km at perihelion in early January and 152.1 million km at aphelion in early July.
Which planet has the most eccentric orbit?
Mercury, with e = 0.206. Its distance to the Sun varies between 46 and 70 million km. Among the dwarf planets, Pluto's eccentricity is higher still, about 0.25.
Can an orbit have an eccentricity greater than 1?
Yes. Such an orbit is a hyperbola: the object is not bound to the Sun and leaves the solar system after one pass. Interstellar visitors such as ʻOumuamua, Borisov and 3I/ATLAS followed hyperbolic orbits.
