want to get into an aerospace grad program, school doesnt have an aerospace program

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im at a crossroads. I want to do aerospace research but we don't have an aerospace department. Is it worth reaching out to other schools to do aerospace research?

I want to go for an MSC in aerospace then eventually PHD. but my school's ME department only has mechatronics stuff. Would it be possible to relate those to an aerospace grad program?

Is it worth reaching out to other schools to join research?