Hello Aspirant
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Yes, ofcourse you should do Aerospace engineering. It has Aeronautical engineering and Astronautical engineering.  Here better to do specialization in these above courses. NASA is national National Aeronautics and Space Administration. NASA's mission is to pioneer the future in space exploration, scientific discovery and aeronautics research. To get into NASA you really need to do alot of hard word .. First of all you need to get into some good engineering institute for aerospace engineering.
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After you are done with graduation, you can sit for the exam, which is held by NASA for the recruitment of scientists and astronauts. Or in order to join ISRO one needs to clear the Joint Entrance Exam which is held by the IITs.
And in order to be a mission specialist, you will need 3 years of related and responsible experience.
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To know which colleges are offering Aerospace engineering course.once visit this below link:
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• https://engineering.careers360.com/colleges/list-of-aerospace-engineering-colleges-in-india

For more information once visit this link below:-

• . https://www.nasa.gov

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If you have any questions further let me know
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Thank you!!