We have already seen that the mass of a star is the most important property in determining a star's structure. For a main sequence star the mass determines the size and temperature. The lifetime of a star on the main sequence depends on the available fuel and the rate at which that fuel is being consumed - the luminosity. Both of these quantities depend on the star's mass, so the lifetime on the main sequence also depends on the mass. When the star uses up its basic supply of fuel, its ultimate fate also depends on its mass. In fact, the mass and the initial composition of a star completely determine its structure and evolution. This can be proven mathematically on the basis of the physical equations involved. This result is known as Vogt's theorem.
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