White Dwarf Radius Calculator Formula

Understand the math behind the white dwarf radius calculator. Each variable explained with a worked example.

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Formulas Used

Radius (R_sun)

radius_solar = 0.0126 * pow(mass_solar, -1/3)

Radius (km)

radius_km = 0.0126 * pow(mass_solar, -1/3) * 695700

Radius (R_Earth)

radius_earth = 0.0126 * pow(mass_solar, -1/3) * 695700 / 6371

Variables

VariableDescriptionDefault
mass_solarWhite Dwarf Mass(M_sun)0.6

How It Works

White Dwarf Mass-Radius Relation

White dwarfs are supported by electron degeneracy pressure. An unusual property: more massive white dwarfs are smaller.

Approximate Relation

R / R_sun ≈ 0.0126 × (M/M_sun)^(-1/3)

A 0.6 M_sun white dwarf is roughly Earth-sized. As mass approaches the Chandrasekhar limit (1.4 M_sun), the radius shrinks toward zero.

Worked Example

A 0.6 M_sun white dwarf.

mass_solar = 0.6
  1. 01R/R_sun = 0.0126 × 0.6^(-1/3)
  2. 020.6^(-1/3) = 1/(0.6^(1/3)) = 1/0.8434 = 1.1856
  3. 03R/R_sun = 0.0126 × 1.1856 = 0.01494
  4. 04R = 0.01494 × 695700 = 10 394 km ≈ 1.63 R_Earth

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