For taking up a career in Space Sciences, you either need to pursue Aeronautical, Avionics or Aerospace Engineering.

Or you may pursue Physics and further research or Postgraduate in Astrophysics.

As far as the first option is concerned, IIST Trivandrum is perhaps one of the best institutes, where you have an option of getting admission without JEE. You need to answer the IIST UG Test and qualify with a great score.

Some of the Top Colleges in Bangalore like RV College of Engineering do have Aerospace Engineering Courses, perhaps you need to answer the COMEDK Exam for this. Bangalore located near to ISRO Facilities and many other upcoming startups in Karnataka and South India, provide excellent scope and impetus to training and placement facilities.

As far as the second option is concerned, you may complete your Graduation in Physics with excellent grades, internships and projects from some of the Reputed Universities, and hence seek admission in Masters (Astrophysics) at some of the Higher Technical Institutes in India or Other Nations.