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The stars are all so far away that they don't feel the Earth's
gravity, so they can't very well 'fall.' They don't even feel
our Sun's gravity, although the planets do of course. The stars
stay in the sky because they are orbiting around the center of
our galaxy, the Milky Way, much like the planets orbit the Sun.
The reason that the stars don't change positions in the sky like
the planets do is because it takes hundreds of thousands of years
for a star to make one orbit, i.e., they do move albeit extremely
slowly by human standards.
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