In Illustrator, a simple **Pattern Brush** will work. Merely drag the art to the **Brush Panel** and choose `Pattern Brush` when asked, then just click `OKAY`. Draw a circle, and click the brush you just made.

[![enter image description here][1]][1]

If you want a bit of spacing between the iterations, extend the no-fill, no-stroke, rectangle in the brush artwork and then update the brush in the **Brush Panel** by holding the <kbd>Option/Alt</kbd> key down as you drag new artwork on top of the existing brush in the **Brush Panel**.

[![enter image description here][2]][2]

The only way to control the amount of iterations is to adjust either the size of the circle, or the size of the brush.

If you double-click the brush artwork in the **brush Panel** you can adjust the scale of the brush. Reducing the scale of the brush will allow for more iterations.

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/mqQA6.png
  [2]: https://i.sstatic.net/jxRPy.png
  [3]: https://i.sstatic.net/BJP6f.png