The word "aerologic" refers to anything relating to the science or study of aerial navigation. When looking for synonyms for this word, one could use a variety of related terms such as "aeronautical", "flight-related", "aviation-focused", or "aircraft-oriented". Other possible synonyms might include "aerial", "airborne", and "sky-related". Depending on the context, one might also consider terms like "pilot-centric", "airfield-oriented", or "atmospheric-focused" as relevant synonyms. Ultimately, the best synonym will depend on the specific usage of the word in question and the intended meaning and audience of the text.