Eddington Luminosity Calculator Formula

Understand the math behind the eddington luminosity calculator. Each variable explained with a worked example.

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Formulas Used

Eddington Luminosity

eddington_lum = 4 * pi * 6.674e-11 * mass * 299792458 / 0.034

In Solar Luminosities

eddington_solar = 4 * pi * 6.674e-11 * mass * 299792458 / 0.034 / 3.828e26

Variables

VariableDescriptionDefault
massObject Mass(kg)1.989e+30

How It Works

The Eddington Luminosity

The maximum luminosity where radiation pressure on infalling matter balances gravitational attraction.

Formula

L_Edd = 4π G M c / κ

Using electron-scattering opacity κ ≈ 0.034 m²/kg for ionised hydrogen. For a solar-mass object, L_Edd ≈ 3.3 × 10⁴ L_sun.

Exceeding L_Edd causes radiation-driven mass loss (stellar winds, super-Eddington outbursts).

Worked Example

A 1-solar-mass object.

mass = 1.989e+30
  1. 01L_Edd = 4π G M c / κ
  2. 02= 4π × 6.674e-11 × 1.989e30 × 2.998e8 / 0.034
  3. 03Numerator = 4π × 3.979e28 = 4.988e29
  4. 04L_Edd = 4.988e29 / 0.034 ≈ 1.47e31 W ≈ 38 300 L_sun

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