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Using ground-based telescopes or the Hubble Space Telescope, astronomers take photographs of galaxies which are many light years from the Earth. Does it mean those photographs are as old as the galaxies are far from the Earth?

As I read that the Universe is growing very radidly, then its position and shape should have changed after many years. Are photographs useless as a result?

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In addition to Rory's answer, studying "old" data is arguably more valuable than if we had access to a single snapshot of the entire visible Universe. By looking out, we are also looking back in time. That means scientists can see how the Universe has changed -- they can compare the structure and behavior of stars and galaxies as they were "just" 100M years old with the structure and behavior as they were 10B years ago.

For instance, we can tell that space was not always expanding at the rate it is now. That's an enormous discovery that we would not have been able to make with a "snapshot" view of the Universe.

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Those photographs are very old - literally, if something is 1 million light years away from us, any photograph we take is 1 million years old. It is that simple.

The photographs are definitely not useless, as we can't travel faster than light - and neither does anything else, so any calculations or assumptions we make based on what we see in these photographs is effectively real for us, as wherever that galaxy is now (a million years later than the photograph) is irrelevant to us - there is no physical way for us to interact with it.

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