Orbital Eccentricity Calculator Formula
Understand the math behind the orbital eccentricity calculator. Each variable explained with a worked example.
Formulas Used
Eccentricity
eccentricity = (apoapsis - periapsis) / (apoapsis + periapsis)Semi-Major Axis
semi_major = (apoapsis + periapsis) / 2Variables
| Variable | Description | Default |
|---|---|---|
periapsis | Periapsis Distance(km) | 147100000 |
apoapsis | Apoapsis Distance(km) | 152100000 |
How It Works
Orbital Eccentricity
Eccentricity describes how elongated an orbit is (0 = circle, approaching 1 = very elongated ellipse).
Formula
e = (r_a - r_p) / (r_a + r_p)
Semi-major axis: a = (r_a + r_p) / 2
Worked Example
Earth: perihelion 147.1M km, aphelion 152.1M km.
periapsis = 147100000apoapsis = 152100000
- 01e = (152.1M - 147.1M) / (152.1M + 147.1M)
- 02e = 5M / 299.2M ≈ 0.01672
- 03a = 299.2M / 2 = 149.6M km
Frequently Asked Questions
What eccentricity is a circle?
A perfect circle has e = 0. Most planets have e < 0.1.
What does e = 1 mean?
Eccentricity of 1 is a parabolic escape trajectory. Above 1 is hyperbolic.
Which planet is most eccentric?
Mercury at about 0.2056 among the eight planets.
Ready to run the numbers?
Open Orbital Eccentricity Calculator