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Planets that orbit very small, cold stars can theoretically be close enough to stay warm – but these perilously close orbits have a few major issues.
The planet will inevitably be tidally locked and always present the same face to the star, freezing one side with endless night and boiling the other.
These small stars are also pretty jumpy. Their internal fusion rates are erratic and they spit huge solar flares off into space. That’s a problem when you’re orbiting close enough to actually get hit by the flares. These planets may have their atmospheres ripped away by solar activity.
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