Re: what is the dark blue ring around planet earth called.

Chris,

I assume you are asking about the blue edge around images of the Earth like this one taken from STS77. This edge is not a ring around the atmosphere, but is actually sunlight scattering off of the Earth's atmosphere, viewed edge-on.

In undergraduate physics, one learns that the sky is blue because light scatters far more strongly off of air molecules at higher (bluer) wavelengths. So if you look up at the sky away from the sun, the blue light reaching your eyes has come from the direction of the sun, but has been scattered towards your eyes by the air molecules in the atmosphere. In the photograph I linked to above, the blue light you see is light from the sun that has been scattered towards the camera by the atmosphere, instead of continuing downwards to strike the planet's surface.

This is not to say that the Earth's atmosphere doesn't have any structure. It does have several distinct layers with different thermal, chemical, movement and density characteristics. This educational page from NASA has a good overview of the atmosphere's different layers.

I hope this helps.