Welcome! Here's a link to a quilt I made with a few of the star-in-star blocks. I didn't know they had a name!
My outer stars finish at 8", inner stars finish at 4".
http://www.quiltingboard.com/picture...t-t209062.html
Before I give you any calculations, i need to know. When you provided the measurements, was that the CUT size of the piece or the FINISHED size of the piece? For instance, you said that the center square was 4.5". Did you cut the piece of fabric 4.5" (cut size) or when you measure the square in one of the completed blocks does it measure 4.5" (finished size)?