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There is a principle in Geography called Tobler's First Law of Geography which states that "Everything is related to everything else, but near things are more related than distant things."

Does this principle apply to star composition? Do stars that are closer together have similar compositions than those that are far apart? I'm guessing that stars that are formed in the same stellar nursery would have similar compositions. Have studies been done to compare the compositions and proximity of stars?

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As you say stars composition depend on the composition of the molecular cloud where they were created. You have a molecular cloud where many stars are being created at the same time, all with the same composition and age, but some are bigger than others. As time goes the bigger stars will die earlier, adding new heavier materials to the cloud which will lead to a new generation of stars with a bigger metalicity.

So the star's composition not only depends on where it was created but also on how old it is.

The best way this can be checked is by studying the stars within a star cluster. You may find this site interesting.

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There have of course been extensive observations of clusters of stars. To all intents and purposes, to the limits of experimental accuracy, it looks like stars that are born in the same open cluster or star-forming region are all born with the same composition. e.g. http://adsabs.harvard.edu/abs/2014A%26A...567A..55S , http://adsabs.harvard.edu/abs/2002AJ....124.2799W , http://adsabs.harvard.edu/abs/2007AJ....133.1161D

There are of course various photospheric abundance anomalies in some stars, but these are normally ascribed to mixing processes or nucleosynthesis within the stars, not their birth composition.

The situation in globular clusters is not so clear cut. Multiple populations distinguished by their chemical compositions have been found. Possibly as a result of ancient mergers. So this does not perhaps represent a violation of Tobler's law since these stars would actually have been born in different environments.

Once stars leave their birth environment then they very quickly become mixed around the Galaxy. A star with a peculiar velocity of only 1km/s will travel a parsec in a million years. Stars born in the same place are probably widely distributed around the galaxy in a billion years or so. Most of the mixing is in azimuth or vertically, rather than Galactocentric radius.

Nevertheless there is a radial dependence (Galactocentric radius) of chemical composition (e.g. http://adsabs.harvard.edu/abs/2010A%26A...511A..56P ). Thus stars with similar Galactocentric radii have similar gross chemical compositions (with some scatter). But then this does violate Tobler's law because it means there is a similarity between objects that are on opposite sides of the Galaxy but with similar distance from the Galactic centre.

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