Solve eccentricity from apoapsis, periapsis, axes, or focus distance quickly today easily. See orbit shape, derived parameters, and downloadable reports for your study projects.
| Case | Known inputs | Computed e | Classification |
|---|---|---|---|
| Nearly circular orbit | rp = 7000 km, ra = 7050 km | 0.003559 | Ellipse |
| Moderate ellipse | a = 10, b = 8 | 0.600000 | Ellipse |
| Highly elongated ellipse | c = 9, a = 10 | 0.900000 | Ellipse |
| Unbound flyby (illustrative) | ε, h, μ chosen so √(1 + 2εh²/μ²) = 1.8 | 1.800000 | Hyperbolic |
Eccentricity, e, quantifies how far an orbit or conic path deviates from a perfect circle. In two‑body dynamics it is dimensionless and depends on geometry and energy. Small e implies nearly uniform orbital distance, while large e indicates strong variation between closest and farthest approach.
The value of e classifies the trajectory: 0 ≤ e < 1 is an ellipse, e = 0 is a circle, e = 1 is a parabola, and e > 1 is a hyperbola. These regimes matter because they separate bound motion from escape trajectories in idealized Keplerian motion.
When periapsis distance rp and apoapsis distance ra are known, the calculator uses e = (ra − rp)/(ra + rp). This approach is common in astronomy because rp and ra are directly reported for planetary and satellite orbits, and it immediately reveals orbit elongation.
For an ellipse, the semi‑major axis a and semi‑minor axis b define the shape. The calculator applies e = √(1 − b²/a²). This geometric form is useful when you measure an orbit projection, fit an ellipse to data, or work with analytical conic section parameters.
The focal distance c is the center‑to‑focus offset on the major axis. Because c = ae for ellipses, the calculator computes e = c/a. This is convenient when you know the ellipse construction or have c from a conic fit but still need the normalized eccentricity.
In gravitational two‑body motion, eccentricity links to specific orbital energy ε and specific angular momentum h via e = √(1 + 2εh²/μ²), where μ is the gravitational parameter. This method supports bound, parabolic, and unbound cases, as long as units are consistent.
Earth’s orbital eccentricity is about 0.0167, so the orbit is nearly circular. Mercury’s is about 0.206, showing a noticeably elongated ellipse. Halley’s Comet is about 0.967, producing extreme distance swings. Interstellar object 1I/‘Oumuamua had e around 1.2, indicating a hyperbolic flyby.
Alongside e, the calculator reports derived a, b, c, rp, ra, and the semi‑latus rectum p = a(1 − e²) for ellipses. These values help estimate closest approach, farthest distance, and orbit geometry for planning observations, assessing thermal environments, or simplifying trajectory calculations. For spacecraft, combining p with inclination and periapsis constraints improves safe clearance and targeting accuracy overall.
It means a perfect circle. The distance from the focus is constant, so periapsis and apoapsis are the same.
In standard orbital mechanics, eccentricity is non‑negative. A negative result usually indicates inconsistent inputs or a sign convention error in the underlying parameters.
The formula combines ε, h, and μ. If their units do not match a single system, the computed quantity under the square root becomes meaningless.
For ideal two‑body motion, 0 ≤ e < 1 is bound (elliptic). e = 1 is parabolic escape, and e > 1 is hyperbolic escape.
It is accurate if rp and ra are measured correctly and refer to the same focus. Small measurement errors can matter when ra and rp are very close.
In real systems it can. Perturbations from other bodies, drag, thrust, or non‑spherical gravity can slowly change orbital elements, including eccentricity.
Some derived quantities assume an ellipse. If your method implies a non‑elliptic case, or a required value cannot be inferred, those fields are left blank.
Accurate eccentricity insights support better orbital and conic modeling\.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.