Can We Survive Without the Sun?
Likely not, with current technologies, the world as we know it would incur a mass extinction of most humans due to lowering temperatures, water bodies freezing, and gravitational instability.
Sometimes, the idea of something that is not possible is a lot of fun, such as what happens to the planet if the Sun simply disappears. It is no surprise to wonder about the consequences after the Sun goes away. If the Sun were suddenly to vanish, the Earth and other planets would maintain their forward momentum, essentially flying outwards in a straight line toward space.
The gravitational pull on Earth and the rest of our Solar System would be affected, and -- without the Sun's steady energy input -- Earth would begin to drift outwards in space. It would take until about eight-and-a-half minutes after the Sun had officially called it a night for the last beams of sunlight to reach ice-covered Earth, starting at this precise point. We might all begin saying goodbye to outdoor crops and the plant life that we depend upon for our food as photosynthesis will cease to occur. Even though the Earth has a molten core, which basically acts as a nuclear reactor, that would still not be enough to combat the entire planet-wide freezing.
How Long Can We Survive Without the Sun?
Most humans could survive for about a week. Within a few days, the temperatures would begin to drop, and any humans left on the planet's surface would die soon after. Within two months, the ocean's surface would freeze over, but it would take another thousand years for our seas to freeze solid.
Although frozen upper layers of the world's oceans would insulate deeper waters beneath, keeping them liquid for hundreds of thousands of years, eventually, they would freeze over as Earth moved towards the steady average global surface temperature of around -400oF. At that point, the atmosphere would have also frozen over and fallen back on Earth, leaving any remaining living people exposed to the brutal cosmic radiation traveling across the cosmos. It would take approximately two months for the surface oceans to freeze and approximately thousands of years for the seas to become fully solid. You should know it takes about 8 minutes for sunlight from the Sun to reach Earth.
If the old Sun's own distended atmosphere actually reached Earth, Earth would be melting within a day. As the aged Sun itself continues to expand, a few of the outward strands of its atmosphere may reach these giants, traveling down gravity wells. Even at distances as far apart as 150 million kilometers (93 million miles), the gravitational tug from the Sun keeps the planet firmly encased in an orbit.
The Sun has a strong gravitational pull on the Earth. For some time, Earth will appear to be like Venus, trapped inside its carbon-dioxide-choked atmosphere. What we actually need sunlight for, what every animal on our planet needs sunlight for, is to create food.
There are only very few exceptions to that, and those animals are living on the bottom of the ocean or in other environments that do not have sunlight. Some bacteria appear capable of living in the extreme cold temperatures in space, so it is likely that some limited bacterial life will remain on the planet. We would experience a loss in the gravitational attraction from the Sun within eight minutes, according to Einstein's theory of general relativity, since gravitational attraction moves at the same speed as light.