We see letters such as $\epsilon$ or $\alpha$ or $\beta$ or $\eta$ etc... (possibly all Greek letters)
Can Somebody state the use of all Greek letters in astronomy?
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The most well known use of Greek letters is in the names of stars created by Johann Bayer in 1603 for his star atlas Uranometria.
Bayer gave each star in his atlas a two-part name. The first part is a greek letter, the second part is the constellation that the star is in (in the Latin genetive form). Generally the brightest star in each constellation is designated "Alpha", the second brightest is Beta and so on.
So Alpha Centauri is the brightest star in the constellation of the Centaur.
There is no general way to answer where Greek letters are used.
There is the Bayer naming convention for (some of) the brightest stars where he named them in each constellation, giving $\alpha$ to the brightest, $\beta$ to the 2nd brightest and so on - but this naming usually stops even before $\omega$ is reached, covering just the brightest few per constellation (and even the ordering is not always strictly by brightness).
In other areas as generally in physics or science in general, Greek letters are used as symbols for certain properties in equations. There do exist conventions like $\varrho$ being used for density, $\alpha$ for kinematic viscosity, etc - but these definitions are not a given nor are they unique. Their meaning has to be established in every context anew; used is what fits the context. Important is only that every reader can know what is meant with each symbol in a given context - thus be consistent throughout your paper or book with their usage.