What is the expected luminosity factor for a star with ten times the solar mass ($10 M_\odot$) using the standard approximation?
Answer
Nearly 3,162 times the Sun's luminosity ($10^{3.5}$)
To determine the expected luminosity for a star ten times the mass of the Sun ($10 M_\odot$) using the common mass-luminosity exponent $\alpha=3.5$, one must calculate $10^{3.5}$. Raising ten to the power of three and a half results in a number close to 3,162. This illustrates the extreme consequences of the power law: an object that is ten times heavier shines more than three thousand times brighter than the Sun, highlighting the intense energy generation occurring within its core due to the exponential sensitivity of fusion rates to mass compression.
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