Well the moon would continue to orbit the Earth, and same for all the moons of the other planets. The planets all have different velocities around the sun, so if the disappearance was instant, they would all set off at different velocities in what ever direction they were traveling when the sun disappeared, so before long they would all be isolated planets traveling alone through the galaxy. Same also for all the asteroids. So there would then, before long, be almost no chance of Earth being hit by an asteroid or comet.
Without the sun, the Earth's atmosphere would freeze, and the surface of the oceans freeze over. The ocean would also. But water has a high thermal inertia, so the oceans would remain liquid for many thousands of years before they also froze. Creatures at the oceans depth, in hydrothermal vents, would hardly notice anything because the hydrothermal vents would continue, and there would be oxygen in the water still.
Eventually then the oxygen in the remaining unmelted parts of the oceans would all be used up, and then the only creatures that survive would be anaerobes, creatures that don't need oxygen.
The Earth's center would remain molten and continental drift would continue to operate and volcanoes, as before. So I think you would continue to have some life in the hydrothermal vents and around the volcanoes where they are warm at least for many millions of years.
Longer term, the Main problem would be how the life would get from one to the next. Once a hydrothermal vent becomes inactive and when a new one forms, how would the life get from one to the next?
Maybe there would be enough heat supplied from the Earth though to keep some areas of the ocean floor liquid. After all, lake Vostock is liquid, beneath a thick layer of ice, with almost no heat supplied from the sun.
In the rest of the solar system, the oceans that are sustained by tidal effects, such as Europa, in orbit around Jupiter and Enceladus around Saturn would remain liquid. If there is any life in these oceans, its habitat would be pretty much unchanged.
Though stars can't just "disappear" like that, planets can get ejected from a solar system. Easiest for the lighter planets. In our solar system, Mercury is the one most likely to be ejected. Stable orbit for now and for several hundred million years probably - but it happens to have a resonance with the giant planet Jupiter (similar rate of precession of its perihelion) - and though the two planets are out of sync right now, from time to time they get into sync and this can gradually change the orbit of Mercury, make it more elliptical so that eventually it could intersect with the orbit of Venus. Over longer timescales, there is a tiny chance that it would be ejected from the solar system (with alternatives that it might hit Venus, Earth, Mars, the Sun or Jupiter).
There's also a tiny chance that Mars would get ejected from the solar system as a result of changing orbit of Mercury (because Mars is so light - Venus and Earth are heavy enough so that losing or changing Mercury's orbit or even a direct collision with it would make hardly any difference to their orbits).
Almost certainly none of this will happen, and it's not going to happen in the near future for hundreds of millions of years, but there's a chance of a few percent that either Mercury or Mars would get ejected.
This was much more likely in the early solar system as it was forming, when many planets may have formed and then either got absorbed by the sun or ejected - our solar system may just be the remnants of the last phase of that process.
So - it is quite possible that there are "rogue planets" in interstellar space. And indeed there's indirect evidence that our galaxy has many of these rogue planets.
Alone in Space - Astronomers Find New Kind of Planet - artist's concept of a Jupiter mass planet in interstellar space.
This is perhaps the best candidate so far, actually imaged as a blue dot
Artist's impression of this planet as a video:
This is another example, likely to be a planet rather than a brown dwarf, imaged in the infrared
Astronomers say they've found a rogue planet with no sun
and artist's impression of what this planet might look like:
Some of those perhaps might have life, either the planet itself, or its moons, if it has any. E.g. a Europa or Enceladus around a "rogue Jupiter" in interstellar space would be just about as habitable for life as in our solar system, heated by tidal effects, just as they are here.
It's also possible that a rogue planet could have a global ocean heated by radioactive heat from its interior. For that to happen it needs a thick layer of ice. Earth's ocean is not quite thick enough, probably needs to be ten kilometers thick or thicker. But an Earth size body could also form with a hydrogen atmosphere if there was no sun to blow it away. So in that case it could have a thick insulating layer of frozen hydrogen on top to keep it warm. Life-sustaining planets in interstellar space?
Earth's ocean is probably not deep enough for a thick crust able to keep the ocean liquid except locally in small regions similar to Lake Vostock. Too much heat would escape.
But if it formed as a rogue planet in interstellar space from a gas globule too small to form a star, if that is possible - or if it formed in a brown dwarf system or far from its parent star - then it might retain a thick enough hydrogen atmosphere to have liquid on its surface. Sort of like a mini gas giant, with a rocky core. That would then keep its surface hot enough for liquid water, because hydrogen can also act as a strong insulator to keep in heat. A Guide to Lonely Planets in the Galaxy
Given that these rogue planets may be more common than stars, it's even possible that life is more common on rogue planets than it is on planets with a star, depending on what conditions are needed for life to evolve. But it would probably be harder to detect on rogue planets.
Rogue planets however are also hard to spot even if close to our solar system. An Earth mass rogue planet with a thick hydrogen atmosphere like that could be quite close, and we might not have spotted it yet, perhaps closer even than Alpha Centauri. After all there are thought to be objects in the Oort cloud larger than Pluto. Could there be rogue planets also?
Or for that matter could there be life bearing worlds out in the Oort clouds of our sun, again with oceans kept liquid either through tidal heating or internal radioactive decay based heat? In that case probably with a thick layer of ice to keep them liquid, or else, maybe hydrogen if large enough to retain a thick hydrogen atmosphere during the early solar system.
If so, I haven't seen any calculation and would be hard to do it until you have good estimates of the population and how common these oceans are, and how habitable they are typically. But if you are optimistic about their habitability, they again could easily provide a larger habitable volume for life than the entire inner region of the solar system right out to Pluto :).
See also Can life exist on a planet without a star? – Sean Raymond – Aeon
And wikipedia article Rogue planet which lists some of the rogue planet candidates.
And this very nice youtube video on the topic by Michael Stevens:
I've also added a comment about WHAT ABOUT US, IF IT HAPPENED TO EARTH? see comments section.
You can get this and many more of my answers now as a kindle book:
Simple Questions - Surprising Answers - In Astronomy
Without the sun, the Earth's atmosphere would freeze, and the surface of the oceans freeze over. The ocean would also. But water has a high thermal inertia, so the oceans would remain liquid for many thousands of years before they also froze. Creatures at the oceans depth, in hydrothermal vents, would hardly notice anything because the hydrothermal vents would continue, and there would be oxygen in the water still.
Eventually then the oxygen in the remaining unmelted parts of the oceans would all be used up, and then the only creatures that survive would be anaerobes, creatures that don't need oxygen.
The Earth's center would remain molten and continental drift would continue to operate and volcanoes, as before. So I think you would continue to have some life in the hydrothermal vents and around the volcanoes where they are warm at least for many millions of years.
Longer term, the Main problem would be how the life would get from one to the next. Once a hydrothermal vent becomes inactive and when a new one forms, how would the life get from one to the next?
Maybe there would be enough heat supplied from the Earth though to keep some areas of the ocean floor liquid. After all, lake Vostock is liquid, beneath a thick layer of ice, with almost no heat supplied from the sun.
In the rest of the solar system, the oceans that are sustained by tidal effects, such as Europa, in orbit around Jupiter and Enceladus around Saturn would remain liquid. If there is any life in these oceans, its habitat would be pretty much unchanged.
Though stars can't just "disappear" like that, planets can get ejected from a solar system. Easiest for the lighter planets. In our solar system, Mercury is the one most likely to be ejected. Stable orbit for now and for several hundred million years probably - but it happens to have a resonance with the giant planet Jupiter (similar rate of precession of its perihelion) - and though the two planets are out of sync right now, from time to time they get into sync and this can gradually change the orbit of Mercury, make it more elliptical so that eventually it could intersect with the orbit of Venus. Over longer timescales, there is a tiny chance that it would be ejected from the solar system (with alternatives that it might hit Venus, Earth, Mars, the Sun or Jupiter).
There's also a tiny chance that Mars would get ejected from the solar system as a result of changing orbit of Mercury (because Mars is so light - Venus and Earth are heavy enough so that losing or changing Mercury's orbit or even a direct collision with it would make hardly any difference to their orbits).
Almost certainly none of this will happen, and it's not going to happen in the near future for hundreds of millions of years, but there's a chance of a few percent that either Mercury or Mars would get ejected.
This was much more likely in the early solar system as it was forming, when many planets may have formed and then either got absorbed by the sun or ejected - our solar system may just be the remnants of the last phase of that process.
So - it is quite possible that there are "rogue planets" in interstellar space. And indeed there's indirect evidence that our galaxy has many of these rogue planets.
This is perhaps the best candidate so far, actually imaged as a blue dot
Image by ESO’s New Technology Telescope at the La Silla Observatory of CFBDSIR J214947.2-040308.9 in infrared light. It's the faint dark blue dot right at the centre of the image (not its real colour obviously, this is a photograph taken in the infrared with false colour) . Credit: ESO/P. Delorme.
See: New Rogue Planet Found, Closest to our Solar System
Artist's impression of this planet as a video:
This is another example, likely to be a planet rather than a brown dwarf, imaged in the infrared
and artist's impression of what this planet might look like:
Some of those perhaps might have life, either the planet itself, or its moons, if it has any. E.g. a Europa or Enceladus around a "rogue Jupiter" in interstellar space would be just about as habitable for life as in our solar system, heated by tidal effects, just as they are here.
It's also possible that a rogue planet could have a global ocean heated by radioactive heat from its interior. For that to happen it needs a thick layer of ice. Earth's ocean is not quite thick enough, probably needs to be ten kilometers thick or thicker. But an Earth size body could also form with a hydrogen atmosphere if there was no sun to blow it away. So in that case it could have a thick insulating layer of frozen hydrogen on top to keep it warm. Life-sustaining planets in interstellar space?
Earth's ocean is probably not deep enough for a thick crust able to keep the ocean liquid except locally in small regions similar to Lake Vostock. Too much heat would escape.
But if it formed as a rogue planet in interstellar space from a gas globule too small to form a star, if that is possible - or if it formed in a brown dwarf system or far from its parent star - then it might retain a thick enough hydrogen atmosphere to have liquid on its surface. Sort of like a mini gas giant, with a rocky core. That would then keep its surface hot enough for liquid water, because hydrogen can also act as a strong insulator to keep in heat. A Guide to Lonely Planets in the Galaxy
Given that these rogue planets may be more common than stars, it's even possible that life is more common on rogue planets than it is on planets with a star, depending on what conditions are needed for life to evolve. But it would probably be harder to detect on rogue planets.
Rogue planets however are also hard to spot even if close to our solar system. An Earth mass rogue planet with a thick hydrogen atmosphere like that could be quite close, and we might not have spotted it yet, perhaps closer even than Alpha Centauri. After all there are thought to be objects in the Oort cloud larger than Pluto. Could there be rogue planets also?
Or for that matter could there be life bearing worlds out in the Oort clouds of our sun, again with oceans kept liquid either through tidal heating or internal radioactive decay based heat? In that case probably with a thick layer of ice to keep them liquid, or else, maybe hydrogen if large enough to retain a thick hydrogen atmosphere during the early solar system.
If so, I haven't seen any calculation and would be hard to do it until you have good estimates of the population and how common these oceans are, and how habitable they are typically. But if you are optimistic about their habitability, they again could easily provide a larger habitable volume for life than the entire inner region of the solar system right out to Pluto :).
See also Can life exist on a planet without a star? – Sean Raymond – Aeon
And wikipedia article Rogue planet which lists some of the rogue planet candidates.
And this very nice youtube video on the topic by Michael Stevens:
I've also added a comment about WHAT ABOUT US, IF IT HAPPENED TO EARTH? see comments section.
You can get this and many more of my answers now as a kindle book:
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
4.8m answer views110.3k this month
Top Writer2017, 2016, and 2015
Published WriterHuffPost, Slate, and 4 moreHuffPost, Slate, Forbes, Newsweek, Business Insider, and Science 2.0