Create your very own 'Image Planet' using the Polar Coordinates Filter.

Some experimentation is required to find images that work.  However the technique is rewarding.  This is what you do:
For circular-looking 'planet' the image needs to be square.  There's also a considerable advantage in using a panoramic format, long narrow image as the starting point. Either choose a panoramic picture, or crop a regular landscape format shot to a panoramic style.

This is what you do.....

Choose your image and note the bit depth. Look at the image tab (just below the options bar) for 8 or 16(bit)

Check the dimensions of the image by Image > Image Size (Ctr+Alt+I).

Make a note of height of your image
Also, make a note of the Resolution.

Create a New Document by File > New (Ctrl+N) and set the height and width to the shortest side of your image you've just noted. 

Choose a white background and set the bit depth to match the original

Resolution:  Set either to your original or the required amount (avoid going higher to avoid resampling).  However, if you're making a print, don't fall below 200ppi.

Once you're set, click 'OK' and the new, square, white document appears.

Go to your image

Select > All (Ctrl+A)

Edit > Copy (Ctrl+C)

Go to the New Document

Edit> Paste (Ctrl+V) and a new Layer appears (See below)

Click on the side 'handle' that's beyond the frame and drag to align with the edge' - See below

You may need to 'zoom out' an amount to see the transform frame outline.