How to use it
- Choose what to find: the luminosity, the radius or the temperature.
- Enter the other two quantities. The radius can be in solar radii or kilometres, the luminosity is in solar luminosities.
- Read the result, with the luminosity in watts, the radius in km, the bolometric magnitude and the peak wavelength.
Formulas
- L/L☉ = (R/R☉)² × (T/T☉)⁴, with R☉ = 695,700 km and T☉ = 5772 K;
- R/R☉ = √(L/L☉) ÷ (T/T☉)²; T = T☉ × (L/L☉ ÷ (R/R☉)²)^¼;
- L in watts = L/L☉ × 3.828 × 10²⁶ W;
- M_bol = 4.74 − 2.5 × log₁₀(L/L☉);
- peak wavelength λ = b ÷ T with b = 2.897771955 × 10⁻³ m·K (Wien’s law).
Worked example
A hot star of 1.711 solar radii at 9940 K:
- T/T☉ = 9940 ÷ 5772 = 1.7221, to the fourth power 8.7951;
- (R/R☉)² = 1.711² = 2.9275;
- L = 2.9275 × 8.7951 = 25.7478 L☉, about 9.856 × 10²⁷ W;
- M_bol = 4.74 − 2.5 × log₁₀ 25.7478 = 1.21;
- the peak of its spectrum is at 2.897771955 × 10⁻³ ÷ 9940 = 291.5 nm, in the ultraviolet.
The other way: a star of 100 L☉ at the Sun’s temperature must have a radius of √100 = 10 R☉.
Tips
- Temperature dominates: a star only twice as hot as the Sun at the same size is sixteen times as luminous.
- Giants are bright despite being cool: 100 R☉ at 3500 K gives 1351.9695 L☉.
- The law treats the star as a black body, which is a good approximation for the total power but not for the exact shape of the spectrum.