Apply the Polar Coordinates filter to your pre-composed footage layer by choosing Effect > Distort > Polar Coordinates. In the Effects panel change the type from polar to rect to rect to polar. Set the Interpolation amount to 100% to create your planet. Note that the final result is a circular layer.
Make sure the planet layer is highlighted and press S to reveal the Scale properties. Click on the stopwatch icon to create a keyframe. Right-click on the keyframe and choose Toggle Holding Keyframe. This will prevent After Effects from interpolating between keyframes, giving us a sudden change when we alter the Scale property.
If your composition is going to have music, add this now, then alter the Scale property of the planet layer to match the audio track. We’re working without audio for this tutorial so we’ve changed the scale every second from 2 seconds to 10 seconds. Be bold and scale up to 300% or more for good results.