Well, we wouldn't die instantly. We already survive every day for 8-16 hours without the sun (depending on the season and location). I'm assuming the intent here is to ask what would happen if the sun were to just suddenly cease to exist entirely. In that case, it would take about 8 minutes for anything to happen to us, since the sun's light and gravity both propagate at that speed. At that point the Earth and moon would just continue on in a straight line, no longer in orbit around the sun. Losing the sun's pull might have some nasty effects on plate tectonics, but I'm not sure about that. The earth would slowly begin to cool. It wouldn't be instantaneous; the atmosphere does a decent job of retaining heat for a time. How long you have here depends on the climate and season where you are. If it's the dead of a snowy winter, temperatures would become nearly unbearable in 24-48 hours. If it's summer, you might have several days. This alone ...
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