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If the sun disappeared, we would not know about it for 8 minutes and 20 seconds, at which point the Earth would suddenly move in a straight line on its way out of the solar system.
Findings
Additional insights we found via Vsauce
Because light and gravity travel at finite speeds, we would continue to see the planets beyond Earth in their usual orbital trajectories for some time.
Without sunlight, the Moon would no longer be illuminated.
Without light, photosynthesis would cease, quickly killing off plants, though it would still take thousands of years for us to consume the oxygen present in the atmosphere.
After a week without the sun, average surface temperatures on Earth would be near freezing, but a year later, they would be around -73 degrees Celsius (-100 degrees Fahrenheit).
Any sustained life near underwater volcanoes or underground communities would rely on warmth from Earth's interior, produced from the decay of radioactive elements.
This geothermal energy could keep ocean microbes near the seafloor alive for billions of years, insulated from the harsh conditions of outer space by a layer of ice across ocean surfaces.
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