As time elapsed, my interest just grew up.
my interest grew (or evolved).
(grew how? you'd have to explain, or simply take this sentence out)
I have strong confidence that MIT AeroAstro department is my place
is the perfect learning place for me maybe?
my commitment
my dedication? (find a synonym of commitment since you already used it)
to improve society
parallel structure mistake (to excellence and to improve, see what i mean?)
also, I'd take this out because you'd have to explain what you mean by improve society
huge contributions
..a bit pretentious here? huge...is not the right word. significant? lasting?
to this discipline
what discipline? you talk about the department, but understand that a department has A LOT of disciplines, or majors
to the entire world
this echoes your improve society point, but you'd have to explain...
Overall, it's not a bad essay, but beware that you make a lot of big statements without support. How exactly are you going to change the world? plans? goals? (more specific than "develop new technologies", you could talk about how/what kind of technologies/new aircrafts you could design, and how that will impact the world)
about your worries of exceeding the word limit, you can cut the essay a lot by taking out all the big talk and unecessary details (I would stay up late to see documentaries on TV.) unless they are really important to your thesis.