Hello brother,
The direct answer to your question is YES, but it is highly difficult to get into a reputed college that provides you with such an opportunity.
Actually, this is the doubt of every student, who is fascinated by atomic-science and certain topics of physics such as gravitation, particles, light, and modern physics during their final years in school. I too have a dream to be a cosmologist, and generally speaking, this field develops a career which does not fetch you money, but the satisfaction and adrenaline rush, that a scientist gets is beyond words. But the sad part of this is, you are in the wrong country(I assume you to be an Indian).
India is a country where this field is quite in a dormant state, and there are very limited resources for an individual to practise career in such a field. On top of it, you will have to get a graduation degree in Physics or Mathematics, and pursue masters taking astrophysics as one of the subjects.
According to my research, There are courses in astrophysics, let's start from class 12.
Option 1: Starting right from Class 12:
You should possess a graduation degree to progress in this career. For that: you should prepare for KVPY(Kishor Vigyan Protsahan Yojna) exam. This exam is conducted for entry to IISC(highly reputed college for graduation in Basic physics and astronomy courses). The passed out students are directly placed in ISRO or are given scholarships to pursue their career(maybe you would like foreign masters course). But the thing is the KVPY exam is quite tough and can be assumed to be of a level of JEE advanced. Also, the course of 11th and 12th comes in this exam, 10th class mathematics is also necessary for getting through this. It's an online exam held during October for 11th and 12th class students. You may appear again if you pursue a B.Sc after class 12th. http://www.kvpy.iisc.ernet.in/main/index.htm - official website of kvpy.
The other option is to get into IISC is JEE, For jee main your score should be around-320/360. For jee-advance, you should have a decent score. In case you are biology(PCB) student, NEET is the way. There are several other methods for entry into IISC, but these are only at 12th level.
Option 2: get into IISER/IIAP/IIA-
This is another prestigious chain of government colleges that provide you with a graduation degree in Astronomy or Basic physics. But even this is not easy to get into. the procedure is again through jee mains and advanced. Although they have their separate exams, still it is far more difficult to crack than JEE.
Option 3: Join B.Sc-
In case you are not affected by the rat race of getting into an engineering college and be among one of the 17lakh engineers being produced every year in India, if you have high interest in Astrophysics-Astronomy, you can do a B.Sc -3-year course in Physics or maths from any reputed institute. Institutes like IIT Delhi, IIT Madras, BHU, IIT Kanpur, IIT kgp, and IISc make you stand out from the crowd. They provide you with hands-on experience with software such as STELLER(used in astrophysics) as well as good telescopes, they may provide you with internships at NASA, ISRO, Russian Space org. etc.
Finally, you should pursue a Masters degree in this course(astrophysics) to be eligible for jobs at NASA.
Option 4: Study abroad
In case you consider yourself mature enough and financially sound, the best option would be to study abroad. Foreign universities have specifically designed courses, which develop you better than other local institutes. Their placement process is far better than Indian colleges in terms of Astrophysics branch. visit this link to get top 10 universities for a basic physics course. https://www.topuniversities.com/university-rankings-articles/university-subject-rankings/10-most-improved-universities-physics-astronomy-2018
Option 5: Do B.tech
Well, the last option is, Join B.tech in any of the core streams, such as CSE, ECE, ME. Qualify GATE, ICRB and you may get admitted to IITs, IISC and there do your masters in astrophysics or get admitted to ISRO, through ICRB.
At last, I would say, this is a very underdeveloped field in India. You should try studying abroad if you want to pursue this hobby as a career. But you may also join free crash courses on youtube or other sites such as Coursera etc. can give you knowledge about the topic, and as you know in today's world, skill is above degree. Further, you may search the basic curriculum of any college for Astronomy, and learn each topic on youtube. Although you'll not earn a degree, you'll learn knowledge.
Hope you this solved your doubts.
Regards.
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