Aeronautical engineering dealt with design and development. We were basically exposed to aircraft. Outside the realm of atmosphere is basically known as astronautical engineering. Aerospace engineering in IIT-Madras combines both aeronautical engineering and astronautical engineering because the dynamics of operating an aircraft in outer space is completely different from that in the atmosphere. It is the job of an aeronautical or aerospace engineer to keep the aircraft airborne or goes into outer space.
It is one of the most fascinating subjects you can study. It is all branches of engineering you can think of. If you are a good aeronautical engineer, you would have to be a good mechanical engineer or a good student of thermodynamics. There is no limit to what you can do. We have a president who is an aeronautical engineer, the first man landing on the moon who is an aeronautical engineer, first Indian woman astronaut who is an aeronautical engineer.
Basically, electronics in aviation is avionics. It is job of Avionics engineer to design systems to navigate from point A to point B or in case of a missile it is to design guidance control systems to see that the missile reaches its target and in case of space craft, he/she should be able to control the spacecraft in outer space.
One can get options to work in Defence labs, airlines, aircraft manufacturers, space agencies like ISRO, NASA. The scope is vast. However, getting a degree in aerospace engineering is not necessarily a passport into the NASA or becoming a spaceship pilot. NASA only has American citizens. One can specialize in emerging technologies such as cryogenics, nanotechnology etc.
Aerospace Engineering is one of the two toughest branches offered by any of the IITs. One is Electrical Engineering and the other Aerospace Engineering. Both of them involve the maximum amount of abstract mathematical content. Whether you are in maintenance or design, the scope for error in aerospace is zero. You make an error in design, somebody will pay for it, you make an error in maintenance, somebody will pay with their lives.
As of now only IITs are offering aerospace engineering. But there are some institutes like