Ok, I'm back and fresh!
I'll start with scientific accurate - as much as I can manage
and then put in speculation to change it, at the end!
Ok, if you have a moon/planet with a translucent atmosphere, and assuming you have a normal main sequence star with no fancy debris between star and planet, then because of Rayleigh scattering (light being scattered by objects - gas molecules in this case - much smaller than the wavelength of the light) then Blue is the predominate colour
no matter what you do. In maths terms it's because the scattering is
inversely proportional to the wavelength to the power of four. And the blue end of the visible spectrum has shorter wavelengths than the red end. So red light just isn't as affected.
The other factor is the Rayleigh cross-section of the molecules. The bigger the cross-section the bigger the overall scattering in terms of amplitude and frequencies that it impacts. (again for the Maths peeps, the scattering is
proportional to the cross-section squared - note not as strong as the wavelength dependency) This cross-section is in simple terms a size - but it is not purely a measurement of 'length' of a molecule - it should really be based on QM calculations of where the electrons are etc...
So the bigger the molecule you can put into the air the more of the red end of the spectrum gets scattered,
but it also scatters blue more efficiently as well...
So the range of sky colours you could get from increasing the size of the cross-section of the molecules in the atmosphere are (according to my thinking):
Indigo/Violet*, Blue, Aquamarine, Pale Blue-Green, White**
* Indigo really is Violet which really is dark Blue but Isaac Newton, for mystical reason of his own wanted the visible spectrum to have 7 colours. Lapis Lazuli is a nice word for that end of the spectrum I think.
** Paraphrasing Dulux, with a hint of blue, probably.
Essentially all shades of blue and closely related to blue. White comes about when enough red comes through and balances out some of the blue. Yellow, Orange and Red skies are for sunsets and only for bits of the sky! Not for the normal background.
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Now you could try and infuse the atmosphere with much bigger molecules to try and get more interesting effects. But the problem here is that big molecules tend to be very short-lived in the atmosphere for a variety of reasons - e.g. either they settle back down into the surface or the action of the light will break down the molecule in the atmosphere. And the molecules you'll need ~the same size as the wavelength of the light are really quiet big. Oxygen for example is only about 28 nm (blue light ~450nm).
A further problem here for those of us who want really nice coloured skies is that as larger particles tend to impact all frequencies of light equally so we tend to get more 'cloud'-like light patterns (diffuse white, greys and blacks)
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Case of the top of my head:
-Water-rich planets (i.e. those with open water anywhere in large quantities) will have atmospheres saturated in water vapour. This impacts the sky colour by whitening it. It also means that the planet will have a defacto water cycle that will help to 'wash' out all other impurities.
-Dry planets will have a lot of dust in the air (no water to wash it out). Then the colour of the dust becomes important. Mar's sky is pink because the dust that is constantly whipped up into the air is mainly iron oxide. But, hey what if the surface was mostly copper oxides not iron - then you could have a green sky!
-Coloured polluntants are a possibility, but think of them like a coloured perspex that augments the basic colour of the sky. For example burning soot and petrol gives a brown hue to the air (Years ago I used to work on the top floor of a building in central London and on clear sunny days you could see the boundary layer between the smog - dirty brown and the clean air above it. Yeuk!) On your alien world you could have the plants pump out any sort of colour - but like smog they would probably be restricted to the very low atmosphere.
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Ok finally, if you want a far out SciFi reason for an Orange or Red sky proper...
Then if you have a small gas with a cross-section that is an
imaginary number (you know, have some particle like Unobtanium or IsntRealium
) then I think*** Blue light would get preferentially reflected back and that would leave the red end of the spectrum to flood the sky - hence giving you some pale yellows, oranges and reds. It would need some sort of freaky particle that interacts very strangely with EM fields. Hey it's SF we write, why not...
***Well the equation probably breaks down - but I tried to go for the opposite to let the red light in!