If I studied astronomy what would be approximatelly the number of formulae I would have to learn during the 4 years?

All I can say is "a lot".

You don't have to learn many at all. It is far more important to understand the concepts behind the formulae. You can always quickly look up a formula if you need to. But you cannot quickly dial up instant understanding.

It will take you years to actually understand astronomy at a deep level. But remember: it's never too late to start learning.

You will have to understand and use hundreds, but you will only memorize a handful. Too bad the memorization is the easy part...

if that is your concern, find something else to make your career, like accounting.

many hundreds.

Open a physics textbook and take a look. Then open an advanced textbook of mathematics. Astronomy is heavy on the physics and maths.