I'm no big scientist but without an Earth to Orbit, wouldn't the Space station have just gone flying off into space?
And to say theres this massive world war that can't work together to rebuild the particle accelerator, then how is there 8 Billion people?
Also, something that really annoys me in movies like this, when the lead leaves a message for themselves in another world/time, they never just say "I'm from a different world/time" and it irritates the shit out of me. Atleast with Time travel it can make logical sense not to mention it but the whole "I don't have a lot of time so I have to drag on this sentence with weirdly cryptic shit that might not apply to you but you have to trust these random words from space that will also be seen by anyone else able to pick them up and in no way could ever possibly be misunderstood by you or another person that could never get you in trouble but totally will get you in trouble"