In order to transform a panorama into a planet, you have to create a panorama first. Then you can "bend" this panorama to a circuar shape. Here's how:
In order to create a panorama you have to take a series of shots and stitch them together with a special software.
You'll get the best result when you use a tripod to ensure a perfect horizon (there are even special tripod heads designed for taking panoramas) and set ISO speed and exposure (i.e. aperture and shutter speed) manually to ensure that the images blend perfectly together. If you're not sure which exposure setting is the best, set the camera to auto or program mode, turn toward the brightest area in the landscape and press the shutter half-way through. On the display you will then see the aperture and shutter speed setting your camera would use. Then turn to the darkest area of the landscape and do the same. Take the mean of these two values and set your camera in manual mode accordingly.
Open all the pictures you want to merge with Photoshop. Then click on File > Automate... > Photomerge. The following window will appear:
Click on "Add open images" and press the OK button. Now sit back and relax while Photoshop is aligning the layers and blending the images together automatically. When it's done the panorama will look something like this:
Next we will crop the image. Take the crop tool (C), select the cropping area and click on the checkbox in the top menubar (or simply press enter). For a seamless 360-degree panorama make sure that the left margin begins where the right margin ends, like this:
The next step is the most important one. You have to resize the picture so that the outcome is a square format. To do this, click on Image > Image Size and uncheck the boxes "Scale Styles" and "Constrain Proportions". Then change the height to the amount that is displayed in the "width" field, as demonstrated in the following animation:
After clicking on "OK" your image will look like this:
After that click on Image > Image Rotation > 180�. Your image will change to this:
Next, click on Filter > Distort > Polar Coordinates. Make sure that the checkbox "Rectangular to Polar" is selected and click on OK.
You can fix these flaws by using the spot healing brush tool (J) or the clone stamp tool (S). If the planet does not look spherical, you can also try Filter > Liquify and use the Forward Warp Tool (W) to remove bumps. After retouching your image you can adjust the levels automatically with Image > Adjustments > Levels or by pressing (Ctrl+L) to increase the contrast:
Lastly, rotate and/or flip the image (Image > Image Rotation) and crop it the way you want:
Finally I increased the vibrance and adjusted the levels of the sky (click here to read more about color enhancements), so that my picture eventually looks like this: