Orbital Eccentricity Calculator Formula

Understand the math behind the orbital eccentricity calculator. Each variable explained with a worked example.

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Formulas Used

Eccentricity

eccentricity = (apoapsis - periapsis) / (apoapsis + periapsis)

Semi-Major Axis

semi_major = (apoapsis + periapsis) / 2

Variables

VariableDescriptionDefault
periapsisPeriapsis Distance(km)147100000
apoapsisApoapsis 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
  1. 01e = (152.1M - 147.1M) / (152.1M + 147.1M)
  2. 02e = 5M / 299.2M ≈ 0.01672
  3. 03a = 299.2M / 2 = 149.6M km

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