Given the mass-luminosity relationship, how does the main-sequence lifetime ($ au_{ ext{MS}}$) scale with mass ($M$)?
Answer
au_{ ext{MS}} ext proporcional M^{-2.5}
Since lifetime is determined by the ratio of fuel available ($M$) to the rate it is burned ($L$), substituting $L ext proporcional M^{3.5}$ results in a lifetime scaling inversely proportional to mass raised to the power of $2.5$ ($ au_{ ext{MS}} ext proporcional M/M^{3.5} ext proporcional M^{-2.5}$).
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