https://pic.armedcats.net/2007/11/30/HKDayPanorama.jpg
This was my original image. As you can see it's cloudy, so the background for the planet are in fact those clouds from the original.
The middle (sea) I had to work on a bit because after applying polar coordinates it had some patterns. So I took the original panorama, cropped out just the sea, stretched it to make a square. Then I could see there was some small vertical patterns that I could smooth out pretty easily. Applied polar coordinates, reduced size and placed over the planet. Then I think I copied it once again and set to colour so it glows a bit more.
The overall color change I got with a warming photo filter adjustment layer, set to 100%, and then a blending mode on the layer, can't recall which one exactly.
But again, these were just small adjustments for minor issues with this particular image.
PS: I forgot one thing, actually its pretty obvious and easy to fix, but still. After applying polar coordinates your corners will be have some stretching lines. Of course you'll have to fix that, just pick a colour from their range (usually blue since that'd be your atmosphere part), pick a large soft brush and paint them over.
edit: Here's an example.
https://pic.armedcats.net/2007/11/30/example.jpg
This was just a shot from the ring, MXM in particular.
Anyway, I didn't bother to make this nice, just for illustration purposes that it works with any picture. Of course like I side the wider the batter as you will have more stuff to wrap around. This one I just flipped horizontally and extended my canvas, and then polar coordinates, that was it. You can also see that it helps if you have some foreground on your picture, sea river etc will work better, but then again it depends what you're after.
edit2: Same picture just rotated 180degrees before polar coordinates. Generally speaking you want to rotate your image before polar coordinates, so you have the sky on the bottom of the picture to have that wrapped around the edges. Otherwise your sky will be in the middle and everything else around it, also a nice effect, depends what you want.
https://pic.armedcats.net/2007/11/30/example2.jpg