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Every Sunday I hike to the top of a (modest) local peak before sunrise.  This gives me about an hour of (usually, weather cooperating!) excellent sky observation time.  With the current alignment of Mars, Saturn, and Antares it is easy to locate the position (not an actual visible object, of course) of the center of the Milky Way.  Last Sunday the center (by coincidence) lay directly behind the peak I was climbing.  This made me consider:  if I continued walking at my current pace (~5 km/h) until I actually reached the center of the galaxy (about 8 KPC), it would take me about 5.5 x 10 exp 12 years (check my math). This brought up a much more difficult question.  Would it still be the center of anything?  I know we're going to collide with Andromeda long before this, and perhaps others as well.  Will we be a mega-galaxy by then?  Would the center be much farther away?  Will all the hydrogen by used up by then and all the stars have been born, burned out and become background-radiation cool dwarf star remnants?  Does anyone know what will happen to the Milky Way over this kind of time scale?

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Hi Correcamino and welcome to the forum. I don't think anybody "knows" what will be the state of the universe when you reach the centre of the milky way. Consensus is that our universe is about 13.8 billion years old. What you are asking is to extrapolate what we know from the past more than 5 thousand billion years into the future. The big question is whether the universe is open (ever expanding and ending up in a frozen universe where all fuel has burned out and entropy rules the place), flat (where the expansion slows to a halt) or closed (where gravity wins the battle over entropy and everything ends up in a Big Crunch).

Some observations favour the ever expanding version of the universe while others say that the universe is very close to being flat. The Big Crunch has not many backers right now. Advances in the observation of the past will certainly change the model for the future in the years to come. There is still a lot of unknowns out there. A good time and place to be curious :)

You better start walking - it's a long way!

HJ

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The distance will change between you and the centre. As the universe is expanding, the space between 2 points also increases. And at your pace, which is very slow compared to the expansion of the universe, you will never be able to reach the centre. As for where the centre is, we don't know exactly, but you can see through some simulation of the collusion of both galaxies and get to know where the centre will be.

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3 hours ago, Sai Samarth said:

The distance will change between you and the centre. As the universe is expanding, the space between 2 points also increases. And at your pace, which is very slow compared to the expansion of the universe, you will never be able to reach the centre. As for where the centre is, we don't know exactly, but you can see through some simulation of the collusion of both galaxies and get to know where the centre will be.

Not so. As the Galaxy is gravitationally bound the distances between its components are not subject to the expansion. The same is true of atoms etc. 

Regards Andrew

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