Making the Planet

NB: The image must be first  turned upside down.
Go to Image > Image Rotation > Flip Canvas Vertical

Go to Filter > Distort > Polar Coordinates and select Rectangular to Polar. 

You can alter the viewing percentage scale to inspect the result. 

Click OK.

You'll notice the outer edges have radial lines and there's a distinct line where the ends have joined up.
From this point some editing will be needed to tidy things up.

Use the Clone Tool, Healing Brush or Content Aware Fill (in Edit > Fill menu) to smooth out irregularities within the scene.

To deal with an uneven sky or background you can either erase it or fill the space with something appropriate.  In this example I decided to fill the sky with a better looking sky from my library of useful sky images.  I distorted the sky in the same way as above then added it to the scene.  Using 'Transform' I enlarged the scale then with a Layer Mask 'painted' it around the edges. 

Having made this form of Polar Coordinate image you may wish to experiment with 'Rotatary Distortion' which follows very similar lines yet gives a very different result.

Click on the link below.