Many stars are part of constellations. Due to dark matter the stars have velocities which are nearly the same unregardless their radius of orbit around the centre of the Milky Way. Also, it takes about 200 million years to orbit this centre. But nevertheless the angle from which we look at those stars could change a bit during this orbit. Regarding all these effects, could you say that constellations don't change at all or does it just take a long while? And of course stars could run out of energy and explode and vanish, so that we don't see them anymore. But is this the only way the constellations could change?
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2 Answers
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The constellations change slowly, over thousands of years, due to the proper motion of the stars with respect to the Sun. The main cause of these motions is the orbit of the stars around the centre of our Galaxy (with or without dark matter). This video shows these changes for the constellation of Ursa Major over 400,000 years.
Another way the constellations can change is indeed through stellar evolution $-$ either the birth or death (or brightening/dimming) of stars. However, the timescale for stellar evolution for naked-eye stars is typically hundreds of millions to billions of years (the Sun's life expectancy is around 12 billion years), so that this effect is much slower (and less well predictable).
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Let me make some more general points to clear up some misconceptions.
The Sun orbits around the Milky Way at a speed of around 230 km/s with respect to the Galactic centre (GC), taking around 200 million years to complete a circuit.
Stars at a similar radius to the Sun from the GC orbit at similar, but not identical speeds and may have peculiar motions inwards and outwards or upwards and downwards. These "peculiar" velocities with respect to the Sun have an order of magnitude of tens of km/s and increase as stars get older. In other words, there is a dispersion of velocities, and each star in a constellation has its own peculiar velocity with respect to the Sun and other stars in the constellation.
The stars that make up the visible constellations are generally within around a thousand light years (a few hundred parsecs) of the Sun.
If we take a star that is 100 light years away, moving at 10 km/s tangentially to our line of sight, then that star will move tangentially about 3 light years in 100,000 years. This corresponds to a change in angle on the sky of nearly 2 degrees (4 times the diameter of the full moon). Nearer (and usually brighter) stars will be more badly affected. This gives you an idea of the sort of timescales over which you might expect typical constellations to visibly change, and it is much shorter than both the orbital timescale of the Sun around the Galaxy and stellar evolutionary lifetimes, which are longer than 10 million years for all but the most massive stars.
Astronomers have to routinely take these motions into account by applying corrections for the proper motion of nearby stars, when locating them automatically with telescopes.
