# Calculating the solar spectrum received by a planet

How do I calculate the spectrum of light experienced on the surface of an alien planet? I need it to decide what color the local photosynthetic life will predominantly be.

• Please note that on out own Earth photosynthetic life can be red, brown, green, blue-green or blue, and even (rarely) yellow (as in the case of Acer palmatum "Golden Pond"). Land plants are green because they are descended from green ancestors, using chlorophyll a; not because of the spectrum of solar light, which has actually a maximum in the yellow-green region... – AlexP May 29 '17 at 21:13
• Welcome to WorldBuilding Ettina Kitten! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! – Sec SE - clear Monica's name May 29 '17 at 21:22
• You need Planck's law en.m.wikipedia.org/wiki/Planck%27s_law it describes spectrum emitted by black body of temperature T.Stars are effectively black bodies with temperature in range of thousands of kelvins. After that, you need to research absorption spectra of gasses and cut "ravines" in spectrum at wavelengths corresponding to most abundant gasses. – M i ech May 30 '17 at 6:15

It depends on your star, and the wavelengths that get absorbed by the atmosphere. Here's a graph for Earth:

The yellow bits are the light arriving from the sun, the red bits are what makes it through the atmosphere. Incoming light is a pretty good match to a blackbody spectrum. Different temperature (colour) stars will shift the peak accordingly - but any native creatures will presumably evolve to use the equivalent "brightest" wavelengths for their visible range.

As you can see, although there are parts of the spectrum that are mostly absorbed - especially by water vapour - they tend to be mostly in the infrared part of the spectrum, and the wavelength bands with the highest energy are in the visible and near infrared.

The picture is from Wikipedia, prepared by Robert A. Rohde as part of the Global Warming Art project, licensed under the Gnu Free Documentation license v1.2 or later.

If you're planning to add other gases/compounds into your atmosphere, then it's probably worth looking up spectroscopic data for them to see where the spectral absorbtion bands are.

• So how would I calculate that graph for my planet? – Ettina Kitten May 30 '17 at 1:14
• If you've got an earthlike atmosphere(oxygen, water vapour, CO2) then the dips will be at the same wavelengths. If you've got stuff in the atmosphere that isn't in ours, you'd need to look up spectroscopic absorbtion bands for the new stuff and add appropriate dips at those wavelengths. For the incoming sunlight, work out the black body curve for the temperature of your star; the shape will be similar but the peak will shift to shorter wavelengths for hotter (bluer) stars, or longer wavelengths for cooler (redder) ones. – JerryTheC May 30 '17 at 1:22

The spectrum of light received by your planet will be dependent on two factors: the spectral radiance of the parent star(s) and the atmospheric composition of the planet. The temperature of the star determines its spectrum (as seen from space). The atmospheric composition of the planet will determine which wavelengths of light are scattered and absorbed from the spectra received by the parent star(s).

The spectral radiance of your star may be approximated by Planck's Law:

$B_\lambda (\lambda) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k_B T} }-1}$

where $h$ is planck's constant, $c$ is the speed of light in a vacuum, and $k_B$ is the boltzmann constant, and T is the temperature of your star. If you haven't determined that yet, you may refer to Hyperphysics' Stellar Spectral types. Plotting $B_\lambda$ vs $\lambda$ will produce the spectral plot @JerryTheC referenced in their answer. You may also calculate the wavelength at which the intensity per unit wavelength of the radiation is at a maximum, $\lambda_\max$ using Wien's Displacement Law (explained here):

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

where b is Wiens's displacement constant.

**Note: Wien's displacement law locates the maximum of the spectrum. If the spectrum is Gaussian (bell shaped), then the color will be a mixture of the wavelengths within one standard deviation of $\lambda_\max$. That is the 'normal' of the gaussian $\lambda_\max \pm 1\sigma$ or the blue in this curve.

# Atmospheric Composition

Earth's atmosphere is layered. Since each layer has a different composition, they each scatter different wavelengths. The Ozone layer in the stratosphere scatters UV light. Nitrogen in the Troposphere scatters blue light much more so than green, yellow, and red light (see this). As the light passes through more air, the scattering increases, thereby shifting the color towards smaller wavelengths. This is why the sun at its zenith is yellow, but orange-red at sunrise/sunset.

If the atmospheric composition were to scatter light differently, expect similar results, but at different wavelengths. Unfortunately, I can't provide anything more useful here without foreknowledge of your atmospheric composition, and even then, I am not an (exo)planetary scientist.