The sun is going to die or “burn out” eventually. It is a fact. If that is what you came here to find out, there you go. However, there is a catch. When stars die, they dont simply go out and disappear. No, God had fun creating stars. long before the sun dies (which will happen in another 5 billion years, but dont procrastinate yet) it will start to run out of hydrogen to burn up. It will get hotter and brighter, but it will also begin to shrink. Now the sun’s gravity is whet keeps us close to it, and this sun’s gravity depends on it’s mass. so since it is getting smaller, the gravity will decrease. This also means that we will start to move further and further away from the sun (so the hotter and brighter thing doesnt really even matter to us). But dont worry, you wont have to live like this for too long. The earth will soon turn into a frozen wasteland in which nothing can survive.
Once the sun does eventually use up all its hydrogen, it will collapse onto itself because it has no more power pushing itself out. It will then reverse its old process, and will be fusing helium (which it was producing) back into hydrogen and carbon. Now this produces a heck of a lot more power than the old method, and the sun will expand at amazing speed. it will engulf all the planets, first Mercury, then Venus, and what’s next? You guessed it: Earth. But those few hypothetical survivors of the ice age will be in luck. They won’t have to experience it. They will have a few years of enjoyment after the planet thaws, and then all the rivers and oceans would evaporate and they would almost literally boil to death. Sounds fun, right?
And now, for the grand finale. Once the sun reaches a certain size, It will no longer have enough gravity to hold itself together, and the sun will explode into a big ol’ fireworks display. Of course, it will be accompanied by super hot gases and radiation flying everywhere, which would just add to the excitement. Now, sticking to the theme of hypothetical survivors, after the explosion, everything wouldn’t be fine and dandy. The sun would reform into a white dwarf, about the size of earth, but with the mass of a star. This means that it is so dense that a cubic centimeter of a white dwarf could weigh a few tons! This also means that the gravitational pull is enormous, so you wouldn’t even be able to fly away in a ship. The reason it is a “white” dwarf is because it is superheated, and it is slowly cooling down. Eventually, it would become a black dwarf, which is how it would stay; cold, black, and barren.
It is a fact.