Planet Equilibrium Temperature Calculator Formula

Understand the math behind the planet equilibrium temperature calculator. Each variable explained with a worked example.

Use the Planet Equilibrium Temperature Calculator

Formulas Used

Equilibrium Temperature

eq_temp = star_temp * sqrt(star_radius / (2 * orbital_distance)) * pow(1 - albedo, 0.25)

Equilibrium Temperature (C)

eq_temp_c = star_temp * sqrt(star_radius / (2 * orbital_distance)) * pow(1 - albedo, 0.25) - 273.15

Variables

VariableDescriptionDefault
star_tempStar Temperature(K)5778
star_radiusStar Radius(m)695700000
orbital_distanceOrbital Distance(m)149600000000
albedoBond Albedo0.3

How It Works

Planet Equilibrium Temperature

This is the temperature at which a planet radiates as much energy as it absorbs from its star.

Formula

T_eq = T_star * sqrt(R_star / 2d) * (1 - A)^(1/4)

  • *T_star* = stellar effective temperature
  • *R_star* = stellar radius
  • *d* = orbital distance
  • *A* = bond albedo

    • The factor of 2 (not 4) appears for a rapidly rotating planet that averages flux over the whole surface.

    Worked Example

    Earth: T_star = 5778 K, R_star = 6.957e8 m, d = 1.496e11 m, A = 0.30.

    star_temp = 5778star_radius = 695700000orbital_distance = 149600000000albedo = 0.3
    1. 01T_eq = 5778 * sqrt(6.957e8 / (2 * 1.496e11)) * (0.7)^0.25
    2. 02R / 2d = 6.957e8 / 2.992e11 = 2.325e-3
    3. 03sqrt(2.325e-3) = 0.04822
    4. 04(0.7)^0.25 = 0.9147
    5. 05T_eq = 5778 * 0.04822 * 0.9147 = 254.8 K

    Ready to run the numbers?

    Open Planet Equilibrium Temperature Calculator