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How could a sentient life form move an exoplanet the mass of the Earth?

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Okay. I have been piecing together the elements of another story for my school PDF newspaper (we publish one to a wiki page every two days). Yesterday I asked this question on whether a second habitable planet could evolve life in the solar system and what its location could be if we kept all of the inner planets. Ckersch pointed out in his answer that a planet could orbit stably in the L4 and L5 positions.

I have decided to make this second habitable planet have intelligent life. Technically, in my world the planet will come from out-of-system, meaning it has been a rogue planet for a long time. The intelligent creatures that lived on it have survived and when the planet began to pass our solar system, it entered and the aliens figured out where the stable L4 and L5 points are in the inner solar System. Since their cities and society above ground froze solid soon after exiting their own system, most of the infrastructure for the planet is still semi-viable (explaining why they don't simply jump ship to Earth or Mars).

The point is, they manually moved their whole planet into the L5 zone. My question is, how could one move an Earth-sized planet? Would one use rockets of some sort? Are there any feasible manners in which to do this, assuming my alien race recently discovered how to mass produce and use antimatter as a source of energy?

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This post was sourced from https://worldbuilding.stackexchange.com/q/10860. It is licensed under CC BY-SA 3.0.

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