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. e > 1 means the object follows a hyperbolic path and is not gravitationally bound to the central body. It will pass by once and never return. The interstellar objects 'Oumuamua (e ≈ 1.2) and Borisov (e ≈ 3.36) had hyperbolic trajectories.

Orbital Eccentricity Calculator

Name: Orbital Eccentricity Calculator
Availability: InStock
Author: Nham Vu

Enter apoapsis and periapsis distances to instantly compute orbital eccentricity and classify the orbit as circular, elliptical, parabolic, or hyperbolic.

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

Enter apoapsis and periapsis distances to instantly compute orbital eccentricity and classify the orbit as circular, elliptical, parabolic, or hyperbolic.

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 orbit is classified: e = 0 circular, 0 < e < 1 elliptical, e = 1 parabolic, e > 1 hyperbolic.
A visual orbit shape diagram updates to reflect the computed eccentricity.

Use cases

Verify planetary orbit eccentricities using real Solar System data.
Classify spacecraft trajectories as elliptical, parabolic, or hyperbolic.
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: 2026-06-11 · Reviewed by Nham Vu