Is it possible for the earth to be sucked into a black hole? If so, what would happen?
It depends on the black hole, but with most black holes the Earth would be sucked in a little at a time -- and it would put on an X-ray light show. More details below.
Unfortunately, we will freeze to death before all the exciting stuff happens because first there needs to be a black hole. If it is formed by gravitational collapse, it must have at least the mass of several Suns. Once it does, its gravity will be greater than the Sun's, pulling us out of our orbit.
Astronomers on the planet Remulac, orbiting the star Vega, might witness what we see when the black hole at Cygnus X-1 extracts gas from its companion star (https://tutor.hix.ai): most black holes are much smaller than Earth, so they cannot consume our planet in one shot.
The "X" in "Cygnus X-1" refers to the gravitational energy that would cause the Earthly material to be drawn towards the hole, spiral inwards toward it, and become so hot that it would emit X-rays. Some of the material would be so accelerated that it would be expelled as jets, which the Remulac astronomers could also see.
That way, even though we were doomed, at least our planet would die a glorious death.
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No
There are no stars anywhere close to our solar system other than our sun; the nearest star to Earth is still 4 light years away. Black holes do not just form out of thin air. A star must be at least three times the size of our sun in order to form a black hole.
We would enter orbit around the black hole as part of the Quasar that would form, even if there was a massive enough star nearby that formed into a black hole strong enough to actually pull Earth out of its orbit. We would be so far from the event horizon that we wouldn't even get sucked into it.
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It is theoretically possible for Earth to be drawn into a black hole, in which case gravitational forces would cause the planet to compress and stretch until it eventually collapses.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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