I want to be an Astrophysicist. What should I study? Which degree should I pursue?

I would advise a different path to follow if you are keen on Astrophysics only. I wouldnt advise going for aerospace engineering as they are two different things.

See this. http://www.physics.iisc.ernet.in/~jap/faqs-frame.htm. This is the FAQs given by IISc. JAP is the IISc programme in collaboration with other institutes offering astrophysics.

However one programme that is an integrated one is offered by Indian Institute of Astrophysics who ask for a candidate with three years B.Tech. degree (Post BSc Hons) in Optics and Optoelectronics / Radio Physics and Electronics from CU or B.Tech / BE degree in Electrical/ Instrumentation/ Electronics and Communications /Computer Science/Mechanical Engineering from an institution recognized by AICTE. A candidate with M.Sc degree in Physics / Electronic Science / Applied Mathematics /Applied Physics from a UGC recognized institution is also eligible to apply.

Check details here https://www.iiap.res.in/intphd.htm. so you can do a course which corresponds with the ones specified above, appear for the entrance exam and join the integrated course.

At a very basic level you can choose to do B.Sc. degree in astronomy, astrophysics or physics may qualify you for entry-level jobs in astrophysics. Later you can choose to do Msc course in astrophysics which is required for most research assistant and consulting positions.

A doctoral (Ph.D.) degree in astrophysics is most likley needed if you want to work for a college or university as a teacher or a researcher. You will also likely need a Ph.D. to work in most federal government research positions. Many astrophysicists who have doctoral degrees work as post-doctoral fellows for 3-6 years before finding permanent employment.

So this is the path to be followed after 12th based on your interest and passion in the course.

Profession wise, You can teach physics as a astrophysicist and if not in teaching the other job role involves your majority of the time using computer programs to analyze data, writing research papers and attending meetings.

Good Luck!!