Hi Surya,

Aerospace engineering deals with both designing and manufacturing of aircraft and spacecraft while aeronautical engineering is a part of aerospace engineering which deals with designing of aircraft's. ... “Aeronautical” is where you study the various forces that act on an air borne vehicle in the Earth's atmosphere.

Aerospace Engineering si the branch of Mechanical Engineering which deals with Aerospace Vehicles, ie. vehicles which operate in an atmosphere, this may be done with or without human.

Aeronautical Engineering is the branch of Engineering which include Aerodynamics, Navigation Science, Stability and Control, Performance, Enduranc. In other words it deals with study of fourses in atmosphere.

Hope this will help you.