Inspired by this question, suppose that the Earth decided to move its orbit much further out to reduce the effects of, say, global warming or the effects of a dying sun (or far enough to make this question interesting).
Say that the world, united, built a great rail system that circumnavigated the globe along Earth's orbital plane. On this rail was a device that could be directed and positioned precisely. It was also able to move along its length such that it could be positioned relative to Earth or its orbit, or anything else along Earth's orbital plane. This device was also capable of producing a thrust. It could be nuclear explosions, water ejected at great velocity, rocket plumes, etc.
My assumption is that the Earth would have to take a long-term approach to moving the planet, so the solution would be something that could be sustained over a long period of time
The question is what would be an appropriate ejection mass and over what time period would it take to move the Earth to a reasonable new orbit that would significantly change our climate? The concerns would be the ejection mass itself having a negative effect on Earth's climate or quality of life in general, i.e. nothing that would create a toxic atmosphere.
Interested in the kind of device, where it's ejecta exits (in the troposphere or past the exosphere), its frequency of use (ongoing, every hour, every month, once a year...) and its practicality.