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I know that because of the universe expansion, at some point we will not see any other galaxies from Earth, and we will be able to see only our own galaxy.

Does anyone have an origin or time estimation when will it happen?

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That will never happen. We will always be able to see the galaxies in the Local Group. We won't get separated from them by the expansion of space because the group is bound together gravitationally. But the rest of the galaxies will be beyond the cosmic light horizon in 150 billion years or so.

However, because of the mutual gravitational attraction it's likely that the Local Group will merge into a single giant galaxy. It appears that the Milky Way & the Andromeda galaxy are already on a collision course, and will merge in around 4.5 billion years, about half a billion to a billion years before the Sun starts its red giant phase. The full merger of the group will take a long time, Wikipedia says the median time is around 450 billion years.

Due to the Sun's gradually increasing luminosity, the Earth will be uninhabitable in a billion years or so, and it's likely to get swallowed by the red giant Sun at some stage. But I guess humans may survive elsewhere in the Solar System (or outside it).

For further details, please see Wikipedia's Timeline of the far future.

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    $\begingroup$ So the 150 billion years - this is the answer I was looking for, thanks. $\endgroup$ Aug 23 '20 at 7:06
  • $\begingroup$ This appears to assume something about cosmological parameters. Andromeda and the Milky Way will have a closest approach in 4.5 billion years. The merger may take very much longer. $\endgroup$
    – ProfRob
    Aug 27 '20 at 7:33
  • $\begingroup$ @Rob I just repeated the time given in the linked Wikipedia article, which doesn't mention how long the merger will take, although it says that the central black holes may take millions of years to merge, and it claims that there will be some tidal distortion in ~3.75 billion years. $\endgroup$
    – PM 2Ring
    Aug 27 '20 at 17:25
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    $\begingroup$ Depending on how head-on the collision is, the merger may take tens of billions of years after the first close approach. The error bar is till quite wide. physics.stackexchange.com/questions/574376/… $\endgroup$
    – ProfRob
    Aug 27 '20 at 18:44
  • $\begingroup$ The second point is that depending on the equation of state for dark energy there could be a big rip, in which case the horizon definitely comes within the local group. $\endgroup$
    – ProfRob
    Aug 27 '20 at 18:46

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