Early sailors discovered a gradual change in position of the North Star. This discovery helped to prove that?

Answer 1

...the earth not only was rotating on its axis, but its axis was also rotating, a motion called precession.

Answer 2

Here is your answer.
This finding proves that the Universe is moving, and in the future, the items that you see in the sky at night now will no longer be in the same place.
The Andromeda Galaxy is on a collision course with our Galaxy, but don't worry it will not collide for several million years, but just think of the view the Astronomers will be getting as the galaxy approaches.

Answer 3

This would also happen if the North Star wasn't in perfect alignment with the Earth's axis to begin with.

Answer 4

It's called precession.