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Is the Universe perpetual and does the Universe observe the laws of Thermodynamics


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... and will they continue in space as long as their parent star(s) exist ?

Not necessarily. Planets can be ejected from a solar system by orbital dynamics involving heavier planets or rogue stars. There are many "orphan" planets out there, hurtling through space with no sun. The future of such a planet is independent of the former parent star.

 

Current best models predict the universe will eventually suffer a heat death. Such a universe may be perpetual but there's nothing worthwhile going on.

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