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Here's a YouTube I made showing the evolving shape of the Big Dipper over 300,000 years. Present-day is roughly in the middle of the video.
Proper motion is the apparent motion of a star across the sky, caused by its actual motion through space.
Proper motion is measured by comparing the position of a star in the sky over a period of time, usually several years. This can be done through astrometry, which is the precise measurement of the positions and motions of objects in the sky.
No, proper motion is too small to be observed with the naked eye. It can only be detected through precise measurements and observations using instruments.
Proper motion allows us to study the movement of stars in our galaxy and understand more about their individual motions and the structure and dynamics of our galaxy as a whole.
The proper motion of Ursa Major (Big Dipper) is relatively small compared to other stars, as it is a relatively close group of stars in our own galaxy. However, over a long period of time, its proper motion can still be observed and measured.