Stefan-Boltzmann Luminosity Rechner — Formel

Stefan-Boltzmann Law

The total power radiated by a spherical blackbody:

L = 4π R² σ T⁴

  • σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴ (Stefan-Boltzmann constant)
  • R = stellar radius
  • T = surface (effective) temperature

    • Luminosity depends on radius squared and temperature to the fourth power.

    Lösungsbeispiel

    The Sun: R = 6.957e8 m, T = 5778 K.

    1. L = 4π R² σ T⁴
    2. R² = (6.957e8)² = 4.840e17
    3. 4π R² = 6.079e18 m²
    4. T⁴ = 5778⁴ = 1.115e15
    5. σ T⁴ = 5.670e-8 × 1.115e15 = 6.322e7
    6. L = 6.079e18 × 6.322e7 ≈ 3.843e26 W ≈ 1.00 L_sun