A bit about how I'm making backgrounds:
They're mostly just really simple combinations of sprites (textures) and particle effects. I paint everything in a composite fashion in photoshop (the planet + any particles that will need to fit on top, such as the glowing green ooze on Earth). I use particle systems to get "cheap" animation, using carefully tuned graphs for size-over-lifetime, speed-over-lifetime, and colour/alpha over lifetime.
Both backgrounds have a lot of particle effects going on.
For the sun:
-Glowing ripples growing out to the edge of the sun.
-Inner "bubbles" that throb (grow up/down in size rapidly).
-A corona/lens-flare glow in front and behind the snowflake, to give outer glow effect to the sun.
-Falling snowflakes around the edge of the sun.
For Earth:
-Large "ooze" particle effect on the continents. Spawns a couple particles that very slowly rise up and then down in alpha, to make it look like it's pusling.
-Blue clouds that are slowly wafting to the right, that are "inside" the "cup" (interior) of the planet (the earth texture itself is cut into 3 parts: the top half, the bottom half, and then a "cup" texture that forms the back of the bottom half and sits behind everything else in Z-order).
-Green clouds that sit in front (z-order) and waft off to the right as well.
-An "outer glow" around the entire planet that pulses a bit.
Later I want to add the moon, with a big splatter of green ooze all over it
Not pictured: Australia, floating off to the side a bit: