I need to create something like this, and I don't know how to! How can I create "orbiting" circles around a sphere similar to the symbol for an atom?
You could use the transform effect which would allow you little less adjustment to fine tune the shape of the orbits.
this way all the other orbits are linked to the shape of the first.
then you would object->expand apperance them and cut them to adjust the stacking
I created this effect by placing ellipse that was duplicated and rotated 4 times at 45 degree (30sec operation)
Next, you cut the ellipses to the sub-shapes and place them on top or below the ball shape.