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Which are the best schools in USA for astrophysics?
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I'm leaning towards Princeton right now but which other schools have good astrophysics programs?

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Most schools with strong physics programs will be strong in astrophysics, so you have a lot of usual suspects. From the public schools, UC Berkeley is a big one, as well as UT Austin, Colorado--Boulder, the University of Illinois, Michigan State, and the University of Washington. UC Santa Cruz also seems to have a very good astrophysics program.

For private schools, it's the expected bunch: Harvard, Princeton, Caltech. MIT has a great astrophysics grad program but I don't actually think they have it for undergrads outside of a concentration in physics. For a lot of schools actually, astrophysics will be a concentration in physics you would do for undergrad, and then a graduate program you'd aim to get a Masters or PhD from if you wanted to pursue it further.

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Just doing a quick search, most of the Ivy league schools, with the exception of University of Pennsylvania, have decent astrophysics programs. Outside of the Ivy league schools, MIT is at the top of the list. If you are looking for other potentially less competitive schools, there is University of Texas - Austin. The school is near the Johnson Space Center, so you may have the opportunity to intern at NASA while in college. There is also CalTech, which has some really cool opportunities with the JPL. Keep in mind that astrophysics is a very difficult field and you're aiming for some of the top programs in the world. You always have the option to complete a graduate program for astrophysics and do a physics or an astronomy undergraduate program.

If you want more info I used this site: https://www.usnews.com/best-graduate-schools/top-science-schools/astrophysics-rankings

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The best astrophysics school, in my opinion, is MIT or Colombia. Colombia is the school of the infamous Neil DeGrasse Tyson, and MIT is a top STEM school, which is why I'd say they're the two best schools for astrophysics. Hope this helps!