'nonastrological' is formed in English by the negative prefix 'non-' added to 'astrological' (from 'astrology').

'astrological' comes from Latin 'astrologia' and Greek 'astrologia' (from 'astron' meaning 'star' + 'logia' meaning 'study, discourse'), which passed into Late Latin and Middle English before yielding the modern adjective 'astrological'; 'non-' is a native English prefix of Latin origin used to negate adjectives, and together they form 'nonastrological' in modern English.

Originally, the Greek term meant 'study of the stars'; over time it came to mean practices or claims relating to astrology, and 'nonastrological' now denotes the absence of such relation.