These models do exist, and as you seem to already suspect, the stars that make up each constellation are completely unrelated to each other. This isn’t limited to just the constellations in our Zodiac; all the constellations are made of stars that are completely unrelated to each other. The constellations as we see them are merely alignments of the stars within our galaxy on our night sky, based entirely on our solar system’s location within the galaxy. If we were in a different part of our galaxy, a different arm, or closer in towards the center, our planet would see a completely different set of stars in our night sky.
Orion (not a Zodiacal constellation) is the constellation most commonly used for a demonstration of how unrelated the stars in a given constellation are, partially because it’s so recognizable in the sky, and mostly made of very bright stars, so you can see it even in light-polluted city skies. It’s also a good example because the stars within it are comically unrelated to each other.</p><p>Betelgeuse, the bright red star in Orion’s shoulder is about 640 light years from earth. In contrast, Bellatrix, the other shoulder star, is only 200 light years from earth, three times closer. Mintaka, the rightmost star in the belt, is a whopping 1200 light years away from the earth, twice as far as Betelgeuse. Put all together into a visualization, the constellation does the following when you rotate around it:
This isn’t unique to Orion. Pretty much any constellation you pick would do the same thing. Even a slight shift in perspective away from our solar system will scramble the entire constellation to our eyes. The stars that make up the Big Dipper are also unrelated to each other, though slightly less scattered than those which make up Orion; the seven bright stars that make up the dipper range from 58 light years from Earth to 124 light years from earth, which is still twice as far as the closest star, but means that all the stars in the Big Dipper are closer to us than any of the stars in Orion.
Because the stars in the Big Dipper are so much closer to us than those in Orion, they will appear to move over time much more than anything more distant, which will have apparent motions of almost nothing over time. Since we know what the speed and direction of that speed of each of the nearby stars in the Big Dipper, we can rewind time and predict where these stars will go in the future, and watch where the stars will go, destroying our handy big dipper in the process.
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