quantity

eccentricity

The standard astronomical term for orbital elongation, quantifying deviation from a perfect circle.
6 related articles · 5 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

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Formulas

$$e \cos \omega = \frac{\pi \Delta t}{2P}$$
Eccentricity and argument of periastron from eclipse timing.
What is in the formula
evariableOrbital eccentricity — eccentricity
ωvariableArgument of periastron — argument of periapsis radian
ΔtvariableTime offset in eclipse timing — time offset second
PvariableOrbital period — period second
cosoperatorComputes the cosine of an angle — cosine
$$\dot{\omega} = \frac{6\pi G M}{a(1-e^2)c^2}$$
General relativity predicts periastron advance in binary systems.
What is in the formula
\dot{\omega}variablerate of periastron advance — angular velocity radian per second
Mvariabletotal mass of the binary system — mass kilogram
avariablesemi-major axis of the orbit — length metre
evariableorbital eccentricity — eccentricity
GconstantConstant of universal gravitation. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum. — speed of light = 299792458 metre per second
$$t_{\mathrm{GW}} = \frac{5}{256} \frac{c^5 a^4}{G^3 \mu M^2} (1-e^2)^{7/2}$$
Time for binary to coalesce due to gravitational wave emission.
What is in the formula
t_GWvariableGravitational wave coalescence time — coalescence time second
avariableSemi-major axis of the binary orbit — semi major axis metre
muvariableReduced mass of the binary system — reduced mass kilogram
MvariableTotal mass of the binary system — total mass kilogram
evariableEccentricity of the orbit — eccentricity
cconstantFundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second
GconstantConstant determining the strength of gravitational force — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$j^2 = a(1-e^2)$$
Specific angular momentum squared in Keplerian orbits.
What is in the formula
jvariablespecific angular momentum — specific angular momentum metre squared per second
avariablesemi-major axis — semi major axis metre
evariableorbital eccentricity — eccentricity
$$\Delta\Omega = \frac{4\pi\chi}{(1-e^2)^{3/2}} \left(\frac{r_g}{a}\right)^{3/2}$$
Frame-dragging causes precession of orbital nodes.
What is in the formula
\Delta\Omegavariableprecession rate of orbital nodes — angular velocity radian per second
\chivariabledimensionless spin parameter of central body — dimensionless spin parameter
evariableorbital eccentricity — eccentricity
r_gvariablegravitational radius of central body — length metre
avariablesemi-major axis of orbit — length metre

Related articles · 6

General Relativity2026-08-061 minarXiv:2608.05974express
A Gravitational Needle in a Haystack
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Eccentricity: a magnifying glass for gravitational waves
In May 2020, the LIGO and Virgo detectors picked up a gravitational-wave burst known as GW200105. Among the many similar gravitational waves recorded, this one stood out for an oddity: the orbit of the colliding neutron star and black hole was not a perfect circle, but a stretched ellipse.
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General Relativity2026-05-073 minarXiv:2605.05537express
The Cosmic Roar of Eccentric Orbits
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Why Giant Planets Often Have Slightly Stretched Orbits
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The trace of a short-lived particle is like a signature left in the detector. The particle is born and decays in an instant, but from its trace you can reconstruct its character — whether it's compact like a stone or fluffy like a snowball. That's exactly what this work is about: the authors propose a new way to read such signatures. They noticed that each particle has an angle that links its mass and lifetime.