Welcome Alexandros81!
As we often find with Inkscape, there is more than one way to accomplish a particular goal. Often, the choice comes down to personal preference. But other times, the requirements for reaching the goal for the image decides the choice.
You could put 18 tick marks around the circle, sort of like an 18 hour clock face (I think there's an LPE that will do this), and then snap the little circles to the intersection of the tick marks and the large circle. Or drlarrye's idea is another way to go. But I think I'll give instructions for yet a 3rd way (and I can even think of a 4th way to do it!). (Although the 4th way is probably the easiest, it doesn't seem to be working. Is Object menu > Arrange > Polar Coordinates broken?)
You can start with your existing SVG file, the way it is. Since you mentioned that you achieved the image visually, without precision, you probably want to snap the little circle to the large circle. It looks very close. But for precision, you can configure your snap control bar like in this screenshot (light green buttons are enabled, dark green disabled)
snap-basic.png
(5.32 kB . 30x583)
(viewed 291 times)1 -- Grab the circle with the mouse, and really you'll just have to move it a tiny amount to achieve the snap. You'll see some text pop up to tell you which element was snapped to which target. You should see something like "rotation center to quadrant point". Release the mouse when you see the expected text.
2 -- While it's still selected, click a 2nd time on it, to reveal the rotation center.
3 -- It's a little hard to notice the rotation center, which is a small plus sign or crosshair in the center. But anyway, grab that plus sign with the mouse and drag it straight down. When it gets near the rotation center of the large circle you'll see it snap, and you'll see the text pop up to confirm that a rotation center is snapped to a rotation center. (Note that you can't actually see the rotation center of the large circle while you're trying to snap the rotation center of the small circle to it. So it's a little tricky, but still not hard to do.)
4 -- Next you have a choice whether you want to clone the small circle (group of 2), or just duplicate it. If you think you might want to edit the group again later, choose clone. (Editing the parent of clones, edits all the clones at once.) But if you don't expect to edit them further, use duplicate. (Both are in the Edit menu, or these buttons on the command bar: duplicate
, clone
, or use Help menu > Key and Mouse Ref to find key shortcuts)
5 -- While the duplicate/clone is still selected, open Object menu > Transform > Rotate, and set for 20°, then click Apply.
6 -- If you decided to duplicate, you can duplicate the last circle, and repeat steps #4 and #5, until you finish. If you decided to clone, you need to re-select the orginal circle (group) each time, and then either click Apply in the Transform dialog as many times as necessary, to rotate each clone to the proper amount; or change the degrees each time.
