This might help. It's about both clipping masks and pathfinder effects in AI CS3.
BTW, I found it by doing a search (including the words, "illustrator" and "cs3" along with "clipping mask") at:
Please review the video that I posted. The info that I need is about 3/4 into the video.
The video is for CS4, not CS3.
A clipping mask is made by drawing a shape on top of, or covering the elements of the illustration below that you eventually want to have visible. That's a bit counter-intuitive, you cover up want you want show? Yes!
Draw another ellipse that covers up all of the lower portion of the planet and on the top edge basically matches the curves of the rings. No need to make an exact fit, it can well overlap the planet shape. Select the planet and the top ellipse and go to Object>Clipping Mask>Make. The top portion of the planet which was not covered by your ellipse disappears and the look is that the planet is behind the rings. Here are some photos...
the transparency of the top pink ellipse is not necessary, I added it for instructional purposes only.
Here's what it looks like with the clipping mask on and the masking object selected.
Here's what it looks like in wireframe (outline) view.
Hope that helps