should i give GATE in AE even if i'm an ECE student

okay so nothing is more embarrassing than this, but i just got to know today that a person can gve GATE in a different stream than the one they have in their bachelors, i'm an ece student and i want to pursue the aerospace field. now, i don't hate electronics but honestly even though i'm in my fourth year i still don't really like all the stuff that i have to learn i this field. anyways, i seriously need help and opinions since my parents told me to do what i think is right. so the question is

do i give gate in aerospace engineering? should i take the risk and go with the subject that i have way too much interest in, but the most knowledge i have about physics is only upto what they teach in first of engineering to all the branches. it sounds ridiculously stupid, and i know aerospace ain't no joke, but i've never felt this tempted? excited? thrilled? for anything before. i love space and the fields related to it, i want to pursue higher studies in these subjects, and later on if i get the chance, then also work in defense sector. it's the first time in my life that i finally have the opportunity to go for what i've always wanted. i went for btech inn ece because i thought it would be a great step to get into the field, but i can't seem to develop the kind of interest/passion for this field like i have with physics. so, should i take this ridiculous risk?

also, i've been going downhill with my college grades due to other reasons, and so the first thing my mother said was that i don't study enough for my enough degree, how would i manage this extra field? and i agree with it. i do. and i know gate isn't something you give based on feelings or passion or thrill but, it feels so tempting now. so another question is

will it be worth it? for both mtech and PSU jobs, is it really something i should go for?