Could you create a travelling planet?

Assuming fission thrusters as described here: Would a nuclear fission thruster with continuous fuel injection be possible?, and assuming drilling for the planet's molten mettle core as discussed here: Could you cool the earth's mantle and then bore into it?, and also assuming that people have built self-sustaining environments underground, and won't instantly freeze or starve to death the second the planet moves further from the star, would it be possible to add thrusters to a planet and travel to a different star system by using the unstable elements in it's own core for fuel?

Maybe the main thrusters would be built at one of the poles so that the planets spin is not such a problem. The spin would have to be gradually reduced to make navigation and guidance easier.

Is the star's gravity a major problem or can you just gradually widen your orbit?

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Could you create a travelling planet?

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