astronomy (n.)

late 14c., "calculation and foretelling based on observation of heavenly bodies," from Latin astrologia "astronomy, the science of the heavenly bodies," from Greek astrologia "astronomy," literally "a telling of the stars," from astron "star" (from PIE root *ster- (2) "star") + -logia "treating of" (see -logy).

Originally identical with astronomy and including scientific observation and description. The special sense of "astronomy applied to prediction of events" was divided into natural astrology "the calculation and foretelling of natural phenomenon" (tides, eclipses, dates of Church festivals, etc.), and judicial astrology "the art of judging occult influences of stars and planets on human affairs."

In Latin and later Greek, astronomia tended to be more scientific than astrologia.  In English, the differentiation between astrology and astronomy began late 1400s and by late 17c. this word was limited to the sense of "reading influences of the stars and their effects on human destiny."

And consequently, an Astrology in the World before Astronomy, either in Name or Science. so that ( Non obstante whatever any Astronomer shall oppose to the contrary) Astrology hath the right of Primogeniture. And all the Sober and Judiciously Learned must needs acknowledge the Truth hereof.—Howbeit, it were to be wished that the Astrologer understood Astronomy, and that the Astronomer were acquainted with Astrology: Although I do in truth despair of ever finding many to be so happily Accomplished. [John Gadbury, introduction to "Ephemerides of the Celestial Motions," London, 1672]

It is ... an extremely just observation of M. Comte, that [the study of astrology] marks the first systematic effort to frame a philosophy of history by reducing the apparently capricious phenomena of human actions within the domain of law. It may, however, I think, be no less justly regarded as one of the last struggles of human egotism against the depressing sense of insignificance which the immensity of the universe must produce. [W.E.H. Lecky, "History of the Rise and Influence of the Spirit of Rationalism in Europe," 1866] 

a general term for disciplined studies of ancient astronomies, 1971, from archaeo- "ancient" + astronomy.