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The idea is that since all the stars share a common space velocity, they will appear to move towards a point of common convergence ("vanishing point") on the sky. This is essentially a perspective effect. Using the moving-cluster method, the distance to a given star cluster (in parsecs) can be determined using the following equation:
Any sequence that is asymptotically equivalent to a convergent geometric sequence may be either be said to "converge geometrically" or "converge exponentially" with respect to the absolute difference from its limit, or it may be said to "converge linearly" relative to a logarithm of the absolute difference such as the "number of decimals of ...
This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M ⊙ < M < 55M ⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1. In summary, the relations for stars with different ranges of mass are, to a good approximation, as the following: [2] [4] [5]
The white dwarf luminosity function (WDLF) gives the number of white dwarf stars with a given luminosity. As this is determined by the rates at which these stars form and cool, it is of interest for the information it gives about the physics of white dwarf cooling and the age and history of the Galaxy. [3] [4]
Nevertheless, very hot main-sequence stars are still sometimes called dwarfs, even though they have roughly the same size and brightness as the "giant" stars of that temperature. [21] The common use of "dwarf" to mean the main sequence is confusing in another way because there are dwarf stars that are not main-sequence stars.
If the star lies on the main sequence, as determined by its luminosity class, the spectral type of the star provides a good estimate of the star's absolute magnitude. Knowing the apparent magnitude (m) and absolute magnitude (M) of the star, one can calculate the distance (d, in parsecs) of the star using m − M = 5 log ( d / 10 ...
The plot of a convergent sequence {a n} is shown in blue. Here, one can see that the sequence is converging to the limit 0 as n increases. In the real numbers , a number L {\displaystyle L} is the limit of the sequence ( x n ) {\displaystyle (x_{n})} , if the numbers in the sequence become closer and closer to L {\displaystyle L} , and not to ...
However, when one can observe a red giant star with a known mass, one can calculate the main-sequence lifetime, [4] and thus the minimum age of star is known given that it is in an advanced stage of its evolution. As the star spends only about 1% of its total lifetime as a red giant, [5] this is an accurate method of determining age.