jchylik
commented
2 years ago This could obviously be done by integrating over the curve but that would be beyond the scope of a spreadsheet. There must be a simpler way to approximate the proportion of visible light.
You can try a fairly good approximation. The curve showing the energy emitted for each frequency in the spectrum is described by the Radiation Law. And the good news are that the its approximation ( https://en.wikipedia.org/wiki/Wien_approximation ) is analytically integrable.
So we can calculate illuminance for each frequency band (ie band for frequencies between f_a and f_b) E (f_a, f_b; T) = ((2 L K T)/(c^2 d^2 )) ((h f_a + K T) exp{ - h f_a / (K T)} -(h f_b + K T) exp{ - h f_b / (K T)})
lortordermur
There is no proper illuminance calculation in the planetary habitability calculator, i.e. the incident light flux per area, weighted for human perception.
The calculator so far simply goes and uses the luminosity reduced by the inverse-square law as “illuminance”:
where E(v) = “Illuminance” (Suns), L(1) and L(2) = Star luminosity (Suns) and d = Distance to planet (AU).
Stars feature different wavelength peaks (Wien’s displacement law) and curves correlating with their temperature. To obtain the illuminance, we need to know not only the luminosity and temperature of the star(s) as well as the distance to the planet, but also an estimate of how much of the star’s light is in the visible spectrum. This could obviously be done by integrating over the curve but that would be beyond the scope of a spreadsheet. There must be a simpler way to approximate the proportion of visible light.