'astrogate' originates from modern English word-formation combining the combining form 'astro-' (from Greek 'astron') and a verb-like element modeled on 'navigate' (from Latin 'navigare'), where 'astron' meant 'star'.

'astrogate' developed as a back-formation from the 20th-century science-fiction noun 'astrogation' (formed by analogy with 'navigation'); 'astrogation' itself was modeled on English 'navigation' (from Latin 'navigatio').

Initially it referred specifically to the technical act of plotting or performing star/naval-style navigation in science-fiction contexts, but its current use is the general sense 'to navigate a spacecraft among the stars.'