The standard astronomical term for orbital elongation, quantifying deviation from a perfect circle.Eccentricity is the fundamental measure of how much an orbit deviates from a perfect circle. In astronomy, it is a dimensionless number between 0 and 1 (or greater for hyperbolic trajectories) that describes the shape of an elliptical orbit. An eccentricity of 0 means a perfectly circular orbit, while values closer to 1 indicate increasingly elongated ellipses. This single parameter encodes a wealth of information about a celestial body's history, its interactions with other objects, and the environment in which it formed.
The concept was formalized by Johannes Kepler in the early 17th century, who discovered that planetary orbits are ellipses with the Sun at one focus. The term 'eccentricity' itself derives from the ancient Greek 'ekkentros', meaning 'out of center', referring to the offset of the ellipse's center from the focus.
The eccentricity of an orbit is determined by the orbital energy and angular momentum of the object. In a two-body system governed by gravity, the shape of the orbit is fixed by these conserved quantities. A circular orbit has the minimum possible energy for a given angular momentum; any extra energy stretches the orbit into an ellipse. When multiple bodies interact, gravitational perturbations can exchange energy and angular momentum, changing eccentricity over time. For example, a passing star or a massive planet can 'kick' a smaller body, increasing its eccentricity, while tidal interactions or dynamical friction can circularize orbits.
Eccentricity is used to detect exoplanets (a slight orbital wobble reveals a companion), to predict the timing of transits, and to analyze gravitational wave signals from merging black holes, where the orbital eccentricity leaves a distinct imprint on the waveform.
Mercury has the highest orbital eccentricity of any planet in the Solar System (about 0.206), which was crucial in Einstein's confirmation of general relativity, as it explained the anomalous precession of its perihelion.
| e | variable | Orbital eccentricity — eccentricity |
| ω | variable | Argument of periastron — argument of periapsis radian |
| Δt | variable | Time offset in eclipse timing — time offset second |
| P | variable | Orbital period — period second |
| cos | operator | Computes the cosine of an angle — cosine |
| \dot{\omega} | variable | rate of periastron advance — angular velocity radian per second |
| M | variable | total mass of the binary system — mass kilogram |
| a | variable | semi-major axis of the orbit — length metre |
| e | variable | orbital eccentricity — eccentricity |
| G | constant | Constant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum. — speed of light = 299792458 metre per second |
| t_GW | variable | Gravitational wave coalescence time — coalescence time second |
| a | variable | Semi-major axis of the binary orbit — semi major axis metre |
| mu | variable | Reduced mass of the binary system — reduced mass kilogram |
| M | variable | Total mass of the binary system — total mass kilogram |
| e | variable | Eccentricity of the orbit — eccentricity |
| c | constant | Fundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second |
| G | constant | Constant determining the strength of gravitational force — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| j | variable | specific angular momentum — specific angular momentum metre squared per second |
| a | variable | semi-major axis — semi major axis metre |
| e | variable | orbital eccentricity — eccentricity |
| \Delta\Omega | variable | precession rate of orbital nodes — angular velocity radian per second |
| \chi | variable | dimensionless spin parameter of central body — dimensionless spin parameter |
| e | variable | orbital eccentricity — eccentricity |
| r_g | variable | gravitational radius of central body — length metre |
| a | variable | semi-major axis of orbit — length metre |

