Place copies of a non-rotated star to the wanted places. You can mark the wanted places for ex. by making a 12-gon, 12 cusp star or by rotating & copying straight lines.
You have used different 5 cusp star than Illustrator's default star. I drew one for tests. A placement example:
Select the star prototype. Turn "Show center" =ON in the Attributes panel. Make copies and drag them to the right places by dragging the centerpoint. They should snap if you have option View > Snap to point =ON.
(NOTE: the shown centerpoint is actually the center of the bounding box. It's a little different than the center of the mass which is the crossing of two different symmetry axles of a star)
Group the lines and keep them until you are sure everything is centered properly. You can make them invisible in the layers panel. Also group the stars as soon as you have placed them.
Not asked: You will probably see another problem. It's the apparent non-symmetry, if you place a circle in the middle of the stars:
The center of the circle is at the crossing point of the placing lines and it clearly seems to be at too high. I tested, does it help if the stars are placed by using their mass canters instead of their bounding box centers. It didn't help, the circle seemed to be at too low.
I guess you must finally move the grouped stars upwards purely subjectively. For comparison there's the subjectively fixed version in the right: