Blackbody Peak & Wien's Law

Blackbody Peak & Wien's Law

Stars emit radiation with a spectrum that closely follows a blackbody. The wavelength at which the spectrum peaks is inversely proportional to the surface temperature — this is Wien's displacement law:

$\lambda_{\max} = \frac{b}{T}$

where $b = 2.898 \times 10^{-3}$ m·K is Wien's displacement constant.

Stellar Colors

The Sun peaks in green light — but it also emits strongly across the entire visible spectrum, which is why sunlight appears white.

Luminosity Ratio

For two stars of the same radius at temperatures $T_1$ and $T_2$, the Stefan-Boltzmann law gives:

$\frac{L_1}{L_2} = \left(\frac{T_1}{T_2}\right)^4$

A star at 30,000 K is over 700 times more luminous than a star of equal size at 5,778 K.

Inverse: Temperature from Peak

Given an observed peak wavelength, you can recover the temperature:

$T = \frac{b}{\lambda_{\max}}$

This technique — spectrophotometry — is used to determine stellar temperatures from observed spectra.

Your Task

Implement three functions. All constants must be defined inside each function.

• peak_wavelength_nm(T_K) — returns $\lambda_{\max}$ in nanometres
• stellar_color_ratio(T1_K, T2_K) — returns $L_1/L_2 = (T_1/T_2)^4$ for equal-radius stars
• temperature_from_peak(lambda_nm) — returns $T$ in Kelvin from peak wavelength in nm

Use $b = 2.898 \times 10^{-3}$ m·K.