Proper illuminance formula in planetary habitability calculator

[lortordermur]

Proper illuminance formula in planetary habitability calculator

[jchylik]

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)})

[jchylik]

Reiterating on that, I can fairly easy add a sheet for that, however you have to decide on the sampling:

• selected frequency bands (such as corresponding to ultraviolet, blue, green, ...)
• select the sampling of bands after opening the sheet and generate the list

[lortordermur]

What would be nice would be a calculator (for example "Illuminance" on the "Star" sheet) that could say how much of the star's energy output is in a specific frequency band (as a percentage). Bands would be far-infrared, near-infrared, visible light, UV-A, UV-B etc. The illuminance calculation in the "Planetary habitability" calculator could optionally be updated accordingly, to only take into account visible light.

This is how I can determine it on the fly, however I have not worked on the spreadsheet in quite a while. You could do a fork if you want and add a new calculator, and I pull it in or copy-paste in LibreOffice.

[jchylik]

how much of the star's energy output is in a specific frequency band

That is definitely possible, but there are few more free parameters of a star that determine that.
Still, as the first approximation we can use the black-body emission (i.e. spectral distribution based on temperature only)

could do a fork if you want and add a new calculator, and I pull it in or copy-paste in LibreOffice.

I can try that, with LibreOffice the version might even end up compatible.

[lortordermur]

Nice, I would also test in Google Docs and Excel Online because not all OpenDocument features are 100% compatible between the three. But those are details that can be debugged.

Yes, black-body emission should be sufficient for now.