Blue sky from above

kw: photographs, meteorology

This image is a small clip from a large satellite image found at www.raize.ch, titled "High resolution satellite images of the Yecheng-Western Tibet-Kathmandu-Highway 219".

What piques my interest here is the deep blue tint of the shadows that run diagonally from top left. We are seeing blue sky from above! This is not seen in most satellite images for two reasons: firstly, the vertical relief in most images is small so any bluing of the image is automatically corrected for in the camera, and secondly, there are seldom these deep shadows that allow the blue reflected from the sky above to dominate.

This reminded me of a question I've seen a time or two: "Is the sky blue for planets around stars of different colors?" The answer is, it depends. The sky of Mars, for example, is pink because there is always suspended reddish dust, and the air column is 1/1000th that of Earth. Any blue light scattered by Mars's air is correspondingly fainter and the dust color dominates. But if there were no dust, the sky would be blue, though a very blackish blue.

Now, how about an Earth type planet orbiting a "blue" or "red" star? Clear air takes the light that passes through it and scatters a small proportion of it via Rayleigh Scattering, for which the amount scattered varies as the fourth power of photon energy. Thus, blue with wavelength 450nm is scattered 4.4 times as much as red light with wavelength 650nm. So no matter what the spectrum is of the light passing through a clear gas, the light scattered at right angles will be much bluer. Of course, for a blue star, the light is already blue, and just gets more intensely blue. For a "red" star, we need to realize that even a very cool M9 star is hotter than a carbon arc, which itself is quite a bit hotter than the "whitest" tungsten filament lamp.

There is a contrast effect at work here. The Sun is considered the standard of whiteness by astronomers. The sun's surface temperature is close to 6,500K. Its actual color is rather bluish, compared to the color we see after its light has passed through the atmosphere. Even on the clearest day, at elevations near sea level more than one-third of the light has been scattered, removing lots of blue, so that it has a spectrum more like something at a temperature below 4,000K. There are complications, because stellar gases don't have "flat" emissivity, but I don't want to go into the slight difference between color temperature and actual temperature here.

Any star cooler than the Sun will look yellow or orange by comparison. But the "white" light from a filament lamp (the next generation is likely to forget what they are!) is actually quite reddish, for the filament's temperature is about 2,700K. An M9 star's surface temperature is close to 3,300K, a couple hundred degrees hotter than a carbon arc (used in old-fashioned movie projectors and in searchlights).

If you focus a lot of the "white" light from a tungsten lamp into a beam passing through clean air, and look at the scattered light with a sensitive camera, it will be quite blue. Thus the sky for an Earth type planet around any star will appear blue. If any planet has a green or purple sky, it is because something in the air is changing the spectrum; there's no getting green or purple from a thermal spectrum just by Rayleigh scattering.