If I study astronomy or astrophysics is it true that I dont have to memorise all the formulae..?

No you do not need to memorise formulae. I hate it when colleagues insist on students having to memorise formulae for exams. It is unnecessary. What you need to know if the correct formula to use, where to look it up and to then use it correctly.

Astronomy is mostly Physics. You will need a PhD degree in physics or astronomy. In science, you do not just memorize formulas and plug in numbers. That is jr high stuff. You must learn how to derive the formulas. You must understand the theories and the mathematics. In grad school, you must do original experiments and observations in order to make some new discoveries yourself. 

You don't need to memorize any formulae if your interest is in observational astronomy as an amateur.

Unfortunately the joy of astronomy is far too often quelled by those who want to turn it into a grim, sobering mathathon. Appreciation and understanding is mandatory. Leave the complicated math to those who are paid to learn it. 

But it makes sense to learn the formulae.  Why would you want to study it if you weren't interested in the details?

true , you will never find a job in that field . 

Actually, you learn how the formulas are derived. This, in turn, allows you to create your own formulas for whatever project that you're currently working on.