I can't cross the ocean, but I can travel through seas. I want to know if I have done astronomy research or not (if it makes a difference, I am playing as Haroun al Rashid).
Click the research tab (detailed view). Is in the top left of the screen if I remember it right (looks like a blue Erlenmeyer flask). There you can see the techs you have, tech that can be researched, eras, dependencies, you can create queues, etc.
The researched techs are colored cream-ish.
you can see that agriculture was researched, while pottery etc. can be researched.
Astronomy is in Renaissance era, on the top row if I remember it right, been a while :).