1) Make a circular path and copy it as the motion path for the object. Duplicate a few times and offset each layer (or layer's time).
2) Make 8 copies of the object and link them all to a null in the center. Unlink one layer, rotate, unlink the next, rotate, etc.
3) Make 2 copies of the object at horizontal opposite sides of the circle. Select both and duplicate. Rotate the duplicated pair 90 degrees. Select all and duplicate, rotate the duplicated layers 45 degrees.