The quickest way to answer this question is to say that the stars are not actually fixed in space, they are in fact always moving. But we are also going to explain how astronomers know this and how stars are actually always moving. Since, you came here for an answer.
But they always look so still!
Yes, the stars do look still in the night sky if you look up for a couple of minutes at a time. but they also appear to move and arc in the sky over a period of the whole night-time; this is thanks to the earth’s rotation.
If we take this factor out of the equation, then the stars can look quite still. This is mainly because we are so far away from all of the stars that we can see in the night sky from earth.
The pattern that we can see in the stars has been the same way for hundreds of years; so much so that ancient stargazers actually mapped them and created the constellations that we can still see today.
The Big Dipper has not changed much since it was mapped by stargazers. This goes to show that the stars are bound to appear as if they do not move.
So, how do we know that they are moving?
It is true that the stars appear stationary because we are so far away from them, but they are constantly moving. There are instruments on earth that astronomers use that are sensitive enough to detect the movement of the stars.
We can compare this to driving in the suburbs: the houses that are close to the path and the road will appear to zoom past quickly, but the hills behind them will appear to stay in the same place for a longer period of time.
This is simply because they are further away. But both the hills and the houses are travelling as the same speed relative to the car. This is a perspective effect called parallax.
This is where the further an object is away from you, the less distance it seems to move in your field of view. But that does not mean they are not moving.
How are the stars moving?
The short answer to this is gravity. In space, when you look up to the night sky, the majority of the stars that you can see are within our own galaxy.
Our whole galaxy is orbiting around a black hole, meaning that the stars are constantly moving within the galaxy, just as the galaxy is. These stars are being pulled into a circular orbit that causes them to move.
But this is not the only movement that each star has: as well as every star moving thanks to the gravitational pull of the center of our galaxy, they each have a random galactic motion on top of that, which causes them to move more.
This does not mean that each star has a completely random path that it follows, they do actually have some sort of smooth path or trajectory that is dictated by both the gravitational pull of the center of the galaxy and by the local gravitational field that surrounds the star.
So, each star has a different movement?
Yes! This is because there are different gravitational circumstances for each astronomical body in space. The earth orbits around the sun because of the gravitational pull that the sun exerts on it, and only because the earth is close enough for it to take effect.
And the galaxy revolves around the black hole at the center because of the mass that the black hole possesses. Making its gravitational pull strong enough to command a galaxy’s whole movement.
Each star that is in our galaxy will have different immediate environment and surroundings. Some stars are closer to planets than others, like our sun. This tends to be the case for all solar systems in our galaxy.
Where there is a star, there is like to be a solar system because the gravitational pull of the star will cause asteroids to collide and create planets that will eventually orbit the star.
Therefore, our sun, being a star, will also have a different pattern of movement around space as another star in the galaxy. But this is simply down to the surroundings of the sun compared to other stars.
Conclusion
So, the stars are not fixed in place in the night sky, but the reason that they appear to be is simply due to distance. The stars are so far away that we cannot see them moving due to the parallax effect.
Stars are constantly moving thanks to the center of our galaxy being a black hole that we orbit around, and also thanks to gravitational fields that are local to each individual star that will affect the movement and trajectory of the star.