What if: #1 The Sun disappeared
Everything would seem to be fine for the first 8 minutes. Life would go on as normal and we would be completely oblivious to the impending apocalypse. That’s because light emitted from the Sun would take 8 minutes to reach the Earth and gravity propagates at the speed of light. If the Sun were to suddenly disappear, life would not be extinguished instantaneously but things are going to get real bad, real quick.
8 minutes in and anything that orbits the Sun would fly off in a straight line into space, as they no longer have anything to orbit around. Essentially the objects that orbit the Sun, are moving whilst falling towards the Sun. However they no longer have anything to fall towards and they will continue to move, but now in a straight line.
Lights Out
Those on the night side would only be oblivious to the situation for a few seconds after the day side. The Moon would be plunged into darkness, no longer illuminated be the light of the Sun. The planets one by one will then follow suit slowly extinguishing from view.
With no sunlight plants would begin to struggle. Photosynthesis would stop, however that would only kill some of the plants. There are some trees that can survive for decades without photosynthesis.
Big Freeze
The Earth’s atmosphere retains heat rather well, however without the Suns radiation, things will begin to get rather chilly. Temperatures would begin to drop, and after a few days, temperatures would drop to a hundred degrees or so below zero. Life on the surface would be practically impossible and would likely die off at this point. Within a few weeks, temperatures would be just 50 degrees or so above absolute zero.
It is now likely that the only surviving life would be microorganisms living in the Earth’s crust relying on energy from the Earth’s core. Within a couple of months the surface of the world’s oceans would begin to freeze over, however it would take about a thousand years for the oceans to freeze completely. At around this point the atmosphere will collapse and expose the Earth to harmful cosmic radiation, turning the Earth into a radiated wasteland, devoid of any resemble of what it once was.
Human Survival
It's a grim and dire situation and survival of the human species is unlikely in this scenario. Short term survival would require the ability to maintain heat, and the ability to produce food, both very difficult to achieve without our only abundent energy source. With the surface temperature being so cold, humanity would abandon the surface relocating deep underground, or to the deepest oceans, where there will be warmth from geothermal vents. Thermal heat can used as an energy source. Longer term Humanity would need to evacuate the Earth and set off to find a new home, basking once again in the warmth of a star.
Please let me know how you think Humanity would survive this predicament, and measures you would take for your own survival.
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