Here.
http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003572/8192x4096 would probably be sufficient resolution for a single spherical texture. This one has a 16384x8192 resolution texture available.

You will want a simple spherical skybox for these ones.
Or, if you want to preserve compatibility with older computers (with maximum 2048^2 texture size), you need to do the following:
-map the texture into sphere in 3d modeling program
-take 90 degree field of view images into all cardinal directions (up, down, front, rear, left, right) and use the traditional skybox approach with 6x2048^2 texture size.
Which ever approach you choose to use, this is certainly possible.