In fact: 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.
“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. 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.”
ScienceABC
“The reason stars appear to be stationary if the galaxy is constantly moving is because they are moving at a very slow pace compared to their distance from us. Even though they are moving fast in absolute terms, their motion is negligible when considered on galactic scales.”
Why do stars appear to be stationary if the galaxy is constantly moving →
Astronomy
“Probably the easiest to comprehend is proper motion: the observed rate, as perceived from Earth, of a nearby star sliding along against the background of a seemingly motionless celestial expanse. This motion is mostly apparent: while stars do cruise about on their own paths, the motion is far more noticeable with closer stars, and we measure it according to how dramatic the change appears to us on Earth.”
Las Cumbres Observatory
“This effect can be used to measure the distances to nearby stars. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers can measure a star’s position once, and then again 6 months later and calculate the apparent change in position. The star’s apparent motion is called stellar parallax.”
flerf.org 