Uh, ok, look, light travels at the speed of light, right? So if the red dwarf is 7.8 light years away, the light that bounces off of it or that it generates will hit earth in 7.8 years. However, if that red dwarf were coming right at us, which it is not, it would take (the distance from earth) divided by (the speed of approach) years to hit us.

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Luck? In my experience there is no such thing as 'luck.'