The title sums it up, but I think this could be a tricky question. I first stumbled upon this expression through a song by the German band Haggard, called "Per Aspera ad Astra" (from an album inspired by the life and works of Galileo Galilei, which I highly recommend!). However, whenever I search for references to this phrase, I always find it written as "Ad Astra per Aspera".
Are both semantically equivalent? Which one makes more sense?
Thanks in advance!
Both orders make sense. First of all, it should be noted that Per aspera ad astra can form a complex path and as such its associated unmarked neuter order is indeed quite natural: first VIA (per aspera) and then GOAL (ad astra).
Next, if we take so-called "information structure" into account (vid. https://en.wikipedia.org/wiki/Information_structure), at least two interpretations can additionally be relevant: as for the order Ad astra per aspera, one can assume that ad astra is a topicalized constituent, whereby ad astra is pragmatically interpreted as Topic/Theme and per aspera as Comment/Rheme. Conversely, given the order Per aspera ad astra, the PP per aspera could also be assumed to be topicalized (this reading would be marginal, in my view. As noted above, Per aspera ad astra is better interpreted as involving a complex path with no PP topicalized), whereby per aspera would be Topic/Theme and ad astra would be Comment/Rheme. Essentially, this would be my interpretation of their different information structures, which could, of course, be wrong, since I'm not a native speaker of Latin.
The two are functionally equivalent.
The first means "through difficulties, to the stars", while the latter means "to the stars, through difficulties". In general, Latin word order is extremely fluid (especially in poetry); the functional differences between the two are even more minor than in English.
