As others mentioned the movement of stars around the galaxy just takes such a long time we only see it in the timescale of millions of years.
There are other effects that change the night sky.
Axial precession can be seen in the order of 100 years, with careful measurement.
Not so much the shape of the constellation but where the constellations are relative to the north, and which star is the north star also changes
https://en.m.wikipedia.org/wiki/Pole_star#Precession_of_the_equinoxes
Earth%20goes%20through%20one%20such,equatorial%20coordinates%20and%20ecliptic%20lon
The sun is in the milky way galaxy, funfact, all galaxies are milky ways, and along with the sun, so is every star we see in the sky.
So while the sun has moved quite far in the past thousand years, so did all other stars, at most there would be a 5-15 degree change, but overall it would not be noticed, even if you picked up a roman astronomer and let em see todays night sky.
Each star is moving fast by human being travel standards, but in terms of distances in the universe its EXTREMELY SLOW.
Our galaxy makes a full rotation in about 200 million years. when we’re talking ~2000 years since Roman times, the galaxy has made about 1/100,000th of a full rotation. If you took a photo of our galaxy 2000 years ago, and today, they would look near identical. Keep in mind that the stars we see are ALSO moving with the galaxy, so there really isnt a whole lot of “Scattering”
Because the last time we were in this point in our orbit around the galaxy (a galactic year, if you will), dinosaurs were still around.
Moreover, you can’t see a single star in the sky with the naked eye that is more than 300 light years away. Considering that the galaxy is over 200,000 light years across, that’s a tiny sphere of stars that are all travelling together. Here’s an artist’s rendering of that scale:
https://images.app.goo.gl/V32N9eS6Ly9VEBih9
Bruh we are talking distances of lightyears to millions of lightyears away. Over the timespan of humanity we will not notice the movement of stars and deep sky objects with our naked eye. In contrast with extremely high powered telescopes we can and have detected the movement of stars for example one of the lines of evidence for black holes came from the repeat observations of multiple stars orbiting rapidly around a central object in the centre of the galaxy with has been interpreted to be the event horizon of a black hole
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