The motion of stars is an important and complicated topic in
astronomy. The study of the motions of stars is called stellar
kinematics.
The Sun and all of the stars near the Sun are located in the disk of
the Milky Way Galaxy. The Milky Way consists of billions of stars
in a flat disk that is 70,000 light years in diameter, but only a few
hundred light years thick. All of the stars that you can see at night
are very near to the Sun, in a small patch of this disk. The stars in
the disk are orbiting around the center of the Galaxy, and it takes a
few hundred million years for a star to go all the way around.
The Milky Way is like a giant hurricane, except it is made up of stars
instead of water droplets. The structures and motions are very
similar, however.
So almost all of the stars we can see in the sky (the Sun's neighbors)
are going around the Galaxy on very similar orbits to our Sun's
orbit. There are random differences between the stars' orbits, so the
relative motion appears to be random at first glance.
Keep in mind that the stars are so far apart, that their motion is
extremely difficult to detect. You have to examine their positions
with a very large telescope for many years, even decades, before you
can see their positions change. By doing these careful observations,
astronomers have been able to put together the picture of stellar
kinematics outlined above.
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