Could a habitable planet lit by the cosmic microwave background plausibly exist?
I've got this idea of a rogue planet that is moving that fast through the intergalactic void that the cosmic microwave radiation, thanks to the Doppler effect, actually provides enough heat that it is habitable (and of course, it should be actually inhabited). Thanks to the searchlight effect, I think the incoming radiation should even look roughly star-like, though I haven't done any actual calculation on this.
However I wonder how plausible such a planet would be. In particular,
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Is there any plausible (though possibly very unlikely) way such a planet could come into existence?
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Is it plausible for that planet to exist long enough in this state to develop life? After all, eventually it will have to interact with something else (though I aimed at minimising that by having it pass through an intergalactic void).
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I'd actually also like to have a moon orbiting that planet. Is it plausible for such a planet to have obtained one?
1 answer
A back of the envelope calculation suggests that you need a velocity relative to the CMBR of more than 0.9c. (1mm microwaves blue-shifted to 570nm light typical of yellow dwarves)
This is a problem for several reasons:
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there is no known mechanism to create a planet with that velocity relative to anything
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there is no reasonable mechanism to accelerate a planet to that velocity
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interstellar dust particles, averaging 1 per million cubic meters in the vicinity of Sol, will strike the planet at 0.9c. It's going to be scoured clean in a few decades
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