If the sun were to blow up, life on Earth would
certainly end. It takes eight minutes and twenty
seconds for light to travel from the sun to the
earth, so we would not know that the sun had
exploded until eight minutes and twenty seconds
after the explosion occurred. Most of the energy
from such an explosion would be traveling at the
speed of light or nearly as fast, so life on Earth
would end pretty much as soon as the first of sign
of the explosion arrived.
However this isn't
something you should worry about. The sun has been
burning very steadily for 5 billion years or so,
and won't change very much for another 5 billion
years more. The processes by which stars change is
quite well understood by astronomers, and our sun
will not explode even after 5 billion more years
(only very heavy stars explode) - it will slowly
get bigger, and then slowly get smaller and
gradually emit less and less heat.
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