Hot bodies and the sky

You will write three small functions about the heat and the radio waves of the sky.

The idea. A body at temperature $T$ shines most strongly at $\lambda_{peak} = b/T$ with $b = 2.898 \times 10^{-3}$ m K. A layer of the ionosphere with $N$ electrons in each cubic metre has the critical frequency $f_c = 9\sqrt{N}$ Hz. A planet with sunlight $S$ in W/m² and albedo $A$, and no greenhouse effect, has $T = \left(\dfrac{S(1 - A)}{4\sigma}\right)^{1/4}$ with $\sigma = 5.67 \times 10^{-8}\ \text{W/(m}^2\ \text{K}^4\text{)}$.

Your tasks.

1. In peak_wavelength, return the peak wavelength in m for a body at temperature in K.
2. In critical_frequency, return the critical frequency in Hz for density electrons in each cubic metre.
3. In bare_temperature, return the temperature in K of a planet with sunlight solar and albedo albedo.