If the sun was no more, then Earth would be drawn to a new centre of gravity. The gravity of Earth and the rest of the solar system would be affected and – with there being no constant energy supply from the sun – Earth would start drifting into space.
If the Sun miraculously disappeared, the Earth (and all the other objects in the Solar System) would continue their forward motion in a straight line off into space, instead of following their almost-circular orbits. For the Earth this means it would head off towards the stars at about 30km/s (67,000mph).
Eternal night would fall over the planet and Earth will start traveling into interstellar space at 18 miles per second. Within 2 seconds, the full moon reflecting the sun's rays on the dark side of the planet would also go dark.
Without sunlight, it would be bleak on earth. There wouldn't be any plants, animals and people. There would be no other form of life. No fossil energy sources such as coal, oil and natural gas would be available to generate energy.
With no sunlight, photosynthesis would stop, but that would only kill some of the plants—there are some larger trees that can survive for decades without it. Within a few days, however, the temperatures would begin to drop, and any humans left on the planet's surface would die soon after.
It is the pull of the Moon's gravity on the Earth that holds our planet in place. Without the Moon stabilising our tilt, it is possible that the Earth's tilt could vary wildly. It would move from no tilt (which means no seasons) to a large tilt (which means extreme weather and even ice ages).
Submariners have gone without sunlight for periods exceeding 6-months, using vitamin D supplements. It is unlikely, though, that an adult could die directly and exclusively from prolonged darkness.
If the Sun randomly exploded today or tomorrow, humanity wouldn't survive. However, if the explosion isn't powerful enough and we would know in advance that it will happen, we might have a chance to prolong our existence for a couple of years.
Earth will interact tidally with the Sun's outer atmosphere, which would decrease Earth's orbital radius. Drag from the chromosphere of the Sun would reduce Earth's orbit. These effects will counterbalance the impact of mass loss by the Sun, and the Sun will likely engulf Earth in about 7.59 billion years.
If the moon disappeared, the oceans would have smaller tides. This in turn will affect water organisms like crabs, mussels, starfishes and snails as they depend on the tides for survival. This impact on the coastal ecosystem will lead to an imbalance in the food chain and eventually cause mass extinctions.
This means that the earth would not slow, which then means that the hours of our days would change. Suddenly, without the moon, our days would last between 6 and 12 hours, rather than the 24 hours we experience now.
All of Earth would be in permanent darkness; the air and oceans would retain warmth for some time, but all life would eventually freeze to death.
Within a week, the average global surface temperature would drop below 0°F. In a year, it would dip to –100°. The top layers of the oceans would freeze over, but in an apocalyptic irony, that ice would insulate the deep water below and prevent the oceans from freezing solid for hundreds of thousands of years.
Because of the gravitational force between the Sun and the Earth, the earth orbit around the Sun. If suddenly the Sun vanishes, the gravitational force between the Sun and the Earth will disappear.
Light that's emitted from our host star takes eight minutes and 20 seconds to hit our planet. If the sun suddenly blew up, we actually wouldn't know it happened for — you guessed it — eight minutes, 20 seconds — since even that explosive light show would only be traveling, at maximum, the speed of light.
This is mainly due to the fact that Venus exerts only a very small gravitational influence on the Earth. There may be an increase in the number of meteoric impacts on Earth due to the debris left from the explosion, but I suspect that this would result only in an increase in harmless meteors hitting Earth's atmosphere.
The Sun could not harbor life as we know it because of its extreme temperatures and radiation.
Jupiter: Being a gaseous planet, Jupiter would make for a uniquely uncomfortable life. On — or in? — this enormous planet, "you would descend forever into the gaseous atmosphere until you're crushed by the pressure of the planet's layers."
At the Equator, the earth's rotational motion is at its fastest, about a thousand miles an hour. If that motion suddenly stopped, the momentum would send things flying eastward. Moving rocks and oceans would trigger earthquakes and tsunamis. The still-moving atmosphere would scour landscapes.
If the world's population all met in one place and all ran in the same direction, would this affect Earth's rotation? There would be no detectable effect on Earth's rotation, no matter how fast people accelerate when they start to run. That's because their mass is so much less than that of the planet.