How is one to read אות היא לעולם, נר תמיד and שומר ישראל לעד knowing that the sun will not endure? Torah is written in human language. Is "for ever" confined to human measures, and in fact then, because of the sun, finite? One can say that these references to infinite time are irruptions into human orders of what is genuinely beyond. So does knowledge of the time-bound existence of our star make no difference to reception of the texts of tradition? Or more fancifully, is it a call to space travel?
First, the science. What does science say about the end of days? Well, astronomical observations tell us that our sun is an ordinary star, meaning that it will age and eventually die like all other stars. The earth will have to die with it. So we will have to migrate to other planets to survive. Those planets will also eventually die. Physics tells us that the end of the world is expected to come from the second law of thermodynamics. This law states that entropy always increases, which means that things go inexorably from order to disorder. If you create some order over here, it is compensated by even more disorder over there. So there will come a point when, inevitably, all the atoms in creation will be milling about aimlessly, all carrying the same amount of energy. This means that there will be no concentrations of mass and energy that might bring order. It is called the "heat death of the universe". It is called that because everything will be at the same temperature. It will not happen for a very long time -- at least 100 billion years. It will be a very gentle end, not a cataclysmic one. Unless we learn how to reverse entropy, which does not appear feasible, we cannot avoid it.
Now, Judaism. Judaism agrees with science (the other way around, actually) that the material world is not forever. It is going to end. As for what will happen after it, science is silent, but the Talmud [Berakhot 17a] tells us that after the material world, we will enjoy a spiritual world, where our needs and yearnings will be totally different, in a way that we cannot comprehend today. Maimonides summarizes it as follows:
There are no bodies and no bodily forms in the World to Come… Nor does there occur there any of the events which occur to the human body in this world, such as sitting, standing, sleeping, death, distress, laughter, and so forth, ... no eating or drinking or procreation. The righteous will sit with their crowns on their heads and bask in the radiance of the Divine Presence... There is no way for us in this world to know or comprehend the great goodness which the soul experiences in the World to Come, for in this world we know only of material pleasures, and it is these that we desire. [Rambam, Yad, Teshuvah 8]
The poem Adon Olam, which we sing at end of services, written in the 11th-century, says:
Ve-acharei kichlot hakol levado yimloch nora.
And when everything shall cease, God will still reign in majesty.