Sorry I didn't make it back as fast as I thought. I had to reinstall my operating system. That actually went really smooth, and less than an hour. But when nothing would work, I found out I needed to install a TON of drivers. And that took a really long time.
Anyway, now I can focus a little more. There are a few ways to approach this, and to some extent, it's a matter of personal preference. But if you want a really precise recreation, there probably are a few to 1 way.
Instead of using a filled circle for the objects that will become shadows, use a duplicate of each ring. Ooohh wait....I didn't have time to examine your file earlier. It's made in a different way than I thought. I think it's going to be nearly impossible to make the shadows work, with the design the way it's built.
Hhmmm....Well, maybe it could be done. It will be a little extra work.
Just to explain. I would suggest re-creating it, but instead of using filled circles, make rings. Do it like I exlained above (top of the thread), then you can essentially use a duplicate of each ring for the drop shadow.
Here's what you could try, to make the shadows work with your design. Cross fingers.
1 - Duplicate a circle and remove the filter - also remove the stroke - actually, you should remove the stroke on all the circles
2 - Object menu > Fill and Stroke > Fill tab and click this button
(will automatically create a radial gradient using the same color brown)
3 - Switch to the Gradient tool
4 - Hold Shift and Ctrl key, while you grab one of the outer gradient handles (with the tiny circles on the end) and drag about halfway to the edge of the next biggest circle (the keys make sure the handles don't rotate, and also make sure that both handles move together)
5 - While the handle is still selected, do Shift R (reverses the gradient)
6 - While the outer handle is still selected, you might want to change the color to something a little more gray and maybe darker. If you decide to change the color, you need to do it before the next step
7 - Select the inner handle (the tiny square)
8 - Click this button on the Gradient tool control bar.... hmm, seems I haven't added it to my smiley collection - it's the 2nd to last on the right end, the one with the plus sign (+) (this adds a new gradient stop)
9 - drag that stop outward, and I would drag it just to the outer edge of the yellow (I know it's not exactly an edge, but just so we don't have as much of the shadow on top of the yellow part)(or halfway to the next bigger circle would be fine too)
10 - select the inner (square) handle again and add another new stop
11 - drag it almost to the yellow part of the next smallest circle
12 - almost all of the above can be tweaked and adjusted, but this next part has to be done just like this
13 - duplicate the circle again and remove the gradient and the filter - give it some awful color, to keep from confusing it with the other circles (like neon p ink or neon green) (don't worry, it's going to disappear, but incase you need to undo, it won't get confused with the other circles)
14 - leave it selected, position the mouse over the outer part of the circle, so that you don't accidentally select the wrong circle in the next step
15 - hold Shift and Alt, and click once more - now you should have 2 circles selected - the circle with the gradient, and the bright colored circle
16 - Object menu > Clip > Set (this makes a sharp border for this shadow, so it doesn't bleed over on the next circle.
I'm still in a bit of a hurry, and have to run off again. And it might be tomorrow night before I can get back. So if I've made a mistake in the instructions, Lazur or anyone, please feel free to correct it.
Oh, be sure and group the clipped gradient circle with the opaque parent circle below it. This is a project where it would be easy to accidentally drag a circle out of alignment, and make it really hard to put back in place. And if any of the circles or groups of circles gets moved, it will mess up the whole thing (because of the clipping). So be careful
Just on a quick trial, it looks like that works pretty well. But I'll have to wait until later to double-check the results.
Any questions, feel free to ask
Sorry I'm so short on time lately....