A guide for the Astrology puzzle.
I'd strongly recommend exploring the many different options and discovering this naturally on your own as I did, but if you're frustrated and losing your patience, I wrote this to help others.
How to find the answer:
To figure out the code for the Observatory astrology puzzle, when Sebastian is run out of the tavern you need to follow him, and the way I did it was I didn't let him see me, saw how many times he knocked, knocked the same amount of times, and asked the bookshop lady to allow me in. You can browse her wares and purchase an astrology book that has the direct answer to the puzzle. Not sure if you can get into the bookshop the same way but with different actions but that is what I did. Stealth oriented character.
If you just want the striaght up answer:
You have to add 12 to the first number, add 6 to the second, and subtract 18 from the last number.
So the answer will be 30 16 69.