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Considering how the our solar system, and how every other star in the galaxy is traveling through the cosmos, it seems like it's a miracle that the stars and constellations in the sky stay as constant as they are.

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How is it that the North Star seems to be fixed in space? Is it following our star through space? are we following it? Is it actually moving? Are we getting further away from it? Closer to it? What is our relationship to Polaris in the Galaxy?

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    $\begingroup$ This is a terribly wrong video. Worse than that, it's not even wrong. $\endgroup$ – David Hammen Apr 23 '15 at 23:03
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The relative direction to an object depends mainly on two things:

  • The location of the observer and the object
  • The coordinate system you use to determine direction.

So the first part of that concerns where we are compared with Polaris (and by extension of your question, where the other stars are as well). Yes the stars and other components of the galaxy all have certain motions. But this motion is not large compared to the distances between stars.

Most of the stars we can see in the sky are quite nearby, and are orbiting the galaxy at similar speeds. The speed of the solar system around the galaxy is around $230 km/s$. The relative speed between our sun and nearby stars is much less than that. If we assume that most stars are farther than $5ly$ from us, then we can calculate how long it might take to make a $1\%$ change in distance. $$t = \frac{d}{v}$$ $$t = \frac{4.7x10^{23}m}{2.3x10^5m/s}$$ $$t = 2.06x10^{11}s$$

That works out to over six thousand years. There's a lot of caveats with that number, but it gives you a good idea that for the most part it takes too long for stars to move relative to each other for you to notice during your lifetime without very careful observation.

The second point is that things can move if we change what we mean by "north" or any other direction. North, both on earth and in astronomy, is defined by the rotational axis of the earth. But the axis changes its direction with respect to other stars over time. Besides some smaller scale wobbles, the largest change to the direction of the axis is due to precession and has a period of about 26,000 years. This change will take "north" from a direction that passes relatively near Polaris in a large circle around the sky. With such a long period, again this isn't something to be seen by individuals without detailed measurements.

Precession sky map

So the answer is that people alive today will be able to always think of Polaris as the pole star, but this will be less true for future generations as changes are easily visible on the scale of thousands of years.

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The Sun is of course in motion with respect to other stars in our Galaxy, but it does not move quickly compared with the vast distances involved. For instance it takes about 220 million years for our Sun to orbit the Galaxy once, travelling at around 200 km/s. The stars that are closest to the Sun tend to be orbiting in more-or-less the same direction and at a similar speed (that is why they are in the vicinity of the Sun).

Thinking specifically about Polaris. There are three components of its motion with respect to the Sun - two tangential directions on the plane of the sky and a line of sight velocity.

Using the SIMBAD CDS database we see that Polaris has a line of sight velocity of 16 km/s towards the Sun and tangential motions of 28 km/s in the right ascension direction and 7 km/s in the decreasing declination direction.

This sounds a lot, but a velocity of 1 km/s means it takes about 300,000 years for the star to move 1 light year, and Polaris is about 400 light years from Earth.

So, given its net velocity, the position of Polaris with respect to us will show significant changes (of degrees) on timescales of hundreds of thousands to millions of years.

It is heading southward in the sky, but will take around 25 million years to cross the equator at the rate it is travelling now.

You say that the constellations are "constant". Yes, they are on human timescales, but the motions of the stars both radially and tangentially is routinely measured. If you waited some millions of years, the constellations would look very different.

NB: I am ignoring the precession of the Earth's rotation axis, since this is just a rotation of the coordinate system and not a change of position of the stars with respect to the Earth.

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