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The mass, radius, and luminosity of a star are closely interlinked, and their respective values can be approximated by three relations. First is the Stefan–Boltzmann law, which relates the luminosity ''L'', the radius ''R'' and the surface temperature ''T''<sub>eff</sub>. Second is the [[mass–luminosity relation]], which relates the luminosity ''L'' and the mass ''M''. Finally, the relationship between ''M'' and ''R'' is close to linear. The ratio of ''M'' to ''R'' increases by a factor of only three over 2.5 [[orders of magnitude]] of ''M''. This relation is roughly proportional to the star's inner temperature ''T<sub>I</sub>'', and its extremely slow increase reflects the fact that the rate of energy generation in the core strongly depends on this temperature, whereas it has to fit the mass-luminosity relation. Thus, a too-high or too-low temperature will result in stellar instability.
A better approximation is to take {{nowrap begin}}''ε'' = ''L''/''M''{{nowrap end}}, the energy generation rate per unit mass, as ''ε'' is proportional to ''T<sub>I</sub>''<sup>15</sup>, where ''T<sub>I</sub>'' is the core temperature. This is suitable for stars at least as massive as the Sun, exhibiting the [[CNO cycle]], and gives the better fit ''R'' ∝ ''M''<sup>0.78</sup>.<ref>{{cite web |title=A course on stars' physical properties, formation and evolution |publisher=University of St. Andrews |url=http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC4.pdf |access-date=2010-05-18 |archive-date=2020-12-02 |archive-url=https://web.archive.org/web/20201202003201/http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC4.pdf |url-status=dead }}</ref>
===Sample parameters===
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