Aeronautical Engineering is the field that studies with aerodynamical systems which is supremely bounded to the atmospheric level i.e., it don't deal with outer space devices such as Rockets.

But this fields are very much interrelated so you will find the essence of both in your BE/BTech.

Now for the course you can take admission either in private colleges or government colleges depending on your interest. For Government colleges you have to get good ranks in  JEE MAINS/State level entrances depending on the status of the college. Also some private colleges offer the course and they sometimes accepts the JEE MAINS rank and some colleges takes there own entrances.

Some of the best Aeronautical Engineering colleges (Government):

Dr Ambedkar Institute of Technology, Bangalore

Madras Institute of Technology, Chennai

RTMNU Nagpur - Rashtrasant Tukadoji Maharaj Nagpur University

FGIET Raebareli - Feroze Gandhi Institute of Engineering and Technology

JNTUK Kakinada - Jawaharlal Nehru Technological University

To know more about Government colleges visit the link below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?ownership=Public/Government&degree=B.E%20/B.Tech&branch=Aeronautical%20Engineering

To know more about the Private colleges visit the link below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?ownership=Private&degree=B.E%20/B.Tech&branch=Aeronautical%20Engineering

**You will also get the information for the entrance accepted by each of the colleges, visiting the above provided link.

I hope this answer helps. All the very best for your future endeavors!