Astro is a masculine noun; it means "star" in astronomy or "aster" in botany. Most likely, the original idea was associated with celestial bodies, Astro in Greek, aster in Latin. A combining form must have meaning "about stars or celestial bodies, or activities, taking place outside the earth's atmosphere" - astrology, astronaut, astrophysics, astronomy, dis"aster" :-) But not in the case of astroturf, or what has derived from it. 

The "astroturf" came from "astrodome" in the 1960s. In 1993, it originated the word "astroturfing" - the practice of using "fake grassroots" to influence public opinion. As wiki said, "Astroturf-ing" is the 21st century's version of false advertising. Astroturf made the word "Astro" equal to "fake," at least in combination with "turf." If we apply the same rules to all "Astro"-words, astro-logy becomes a fake-logy; -logy in Latin means "speaking, treatise, science, theory." Astro-nomy - fake-rules (-nomy means a system of rules, laws, or knowledge). How about an astronaut? We are replacing a "star" with "fake," don't we? It's one of those neologisms in English vocabulary that don't make sense. Like strawberry, jackpot, or wedlock.