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I do wonder how do we measure current position of galaxies since all the information transfer speed of the universe is limited by the light speed.

My understanding is the we can only measure the galaxies or stars when the light from them reached to us. For example, we now know Andromeda is approximately 2.5 ml light years away, that means isn't it what we are seeing Andromeda's last 2.5 ml years' position.

And isn't it Andromeda is moving somewhere within those years and we just can't see it yet its current position? If it is so, is it like moving an invisible object toward us?

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Just like how we calculate the distance travelled by a train within a given time period and its average speed.

Yes. Ofcourse the information we get will be of the galaxies' past like in your case (Andromeda galaxy). By varying precision Red shift and Blue Shift and other spectroscopic phenomenon gives us an idea on how fast a galaxy is moving towards or away from us, the nature of the galaxy (Like whether it is interacting with any other galaxies), and the direction it moves all gives a fairly good approximation on the galaxy's position. Although If you take Andromeda galaxy, nothing is going to change much in 2.5 Million years since it is not moving at the speed of light, it is estimated that it moves at a speed of just 113KM per second. For a fair scale, Average speeds of galaxies is 0.75% of speed of light

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