What is orbital eccentricity?

Eccentricity (e) is a dimensionless number that describes the shape of an orbit. e = 0 is a perfect circle, 0 1 is a hyperbola (unbound, escape trajectory).

What are apoapsis and periapsis?

Periapsis is the point in an orbit closest to the central body (perigee for Earth, perihelion for the Sun). Apoapsis is the farthest point (apogee for Earth, aphelion for the Sun). Both are measured from the center of the central body, not its surface.

How is eccentricity calculated?

The formula is e = (r_a - r_p) / (r_a + r_p), where r_a is the apoapsis distance and r_p is the periapsis distance. This is equivalent to the standard conic section definition where e = c/a (focal distance divided by semi-major axis).

Why is Earth's orbit nearly circular?

Earth's eccentricity is about 0.0167, meaning aphelion (152.1 million km) is only ~3% farther than perihelion (147.1 million km). Seasonal temperature variation is caused by axial tilt, not this small orbital eccentricity.

What orbit does a comet typically have?

Long-period comets often have eccentricities very close to 1 (nearly parabolic) or even slightly above 1 (hyperbolic), meaning they pass through the inner Solar System once and escape. Short-period comets like Halley's have elliptical orbits (e ≈ 0.967).

Can eccentricity be greater than 1?

Yes, but an open orbit has no apoapsis, so it cannot be calculated with this two-apsis form. Hyperbolic trajectories require state vectors or parameters such as specific orbital energy and angular momentum.

Orbital Eccentricity Calculator

Enter apoapsis and periapsis distances to compute the eccentricity of a bound circular or elliptical orbit.

Orbital Distances

Solar System Preset

Apoapsis Distance (km)

Farthest point from the central body's center

Periapsis Distance (km)

Closest point from the central body's center

Formula: e = (rₐ − rₚ) / (rₐ + rₚ)
rₐ = apoapsis | rₚ = periapsis

Select a preset or enter custom distances, then click Calculate.

Earth

e = (rₐ−rₚ)/(rₐ+rₚ)

Eccentricity

0.0000

0 (circle) 0.5 1.0 (parabola) >1 (hyperbola)

Orbit Shape (to scale)

Semi-Major Axis

Semi-Minor Axis

Focal Distance

Orbit Type

Distance Summary

Apoapsis (rₐ)

Periapsis (rₚ)

Apo/Peri Ratio

Solar System Eccentricity Comparison

Body	Eccentricity	Shape

Summary

Orbital eccentricity (e) measures how much a bound orbit deviates from a perfect circle. This calculator uses e = (r_a - r_p) / (r_a + r_p), where both apsis distances are measured from the central body's center. Because an apoapsis exists only for a closed orbit, this input method yields e = 0 for a circle or 0 < e < 1 for an ellipse. Open parabolic and hyperbolic trajectories require other orbital parameters.

How it works

Select a Solar System preset to load known apoapsis and periapsis values, or choose Custom to enter your own distances.
Enter the apoapsis distance (farthest point) and periapsis distance (closest point) in kilometers.
The calculator applies e = (r_a - r_p) / (r_a + r_p) to compute eccentricity.
The bound orbit is classified as circular when e = 0 or elliptical when 0 < e < 1.
A visual orbit shape diagram updates to reflect the computed eccentricity.

Use cases

Verify planetary orbit eccentricities using real Solar System data.
Classify bound spacecraft trajectories as circular or elliptical.
Understand how comets differ from planets in terms of orbital shape.
Calculate the eccentricity of transfer orbits for mission planning exercises.
Compare how circular Earth's orbit is versus Mercury's elongated path.
Study orbital mechanics for physics or astronomy courses.
Explore how highly eccentric orbits differ visually from nearly circular ones.
Validate orbital parameters calculated from observational data.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu