There is a Chinese science fiction movie that is about this (although instead of slightly shifting the earth’s orbit, they make earth a spaceship itself) called

There is a Chinese science fiction movie that is about this (although instead of slightly shifting the earth’s orbit, they make earth a spaceship itself) called The Wandering Earth. I believe it is on Netflix. The subtitles for the theatrical release were not the best I’ve ever seen but it was a fun movie.