## toxicsugar22 5 years ago The lifetime of a star is rougly inversly propotional to the cube of its mass. Our sun, which has a mass of 1 solar mass, will last for approxamatly 10 billion years. How long will a star that is half as massive as the sun last?

Let T be the lifetime and M the mass. You're told that the lifetime, T, is roughly inversely proportional to the cube of the mass, M; that is,$T \approx \frac{k}{M^3}$where k is some constant of proportionality. We can compare, then, the lifetime of two stars as, $\frac{T_2}{T_1}\approx \frac{\frac{k}{M_1^3}}{\frac{1}{M^2_3}}=\frac{M_1^3}{M^3_2}$From the information, you have that the mass of the other star will be $M_{Star}=\frac{1}{2}M_{sun}$so,$\frac{T_{Star}}{T_{sun}}\approx \frac{M^3_{sun}}{(\frac{M_{sun}}{2})^3}=2^3=8$So the lifetime of the star is approximately,$T_{Star}\approx 8T_{sun}=80 \times 10^9yr$that is, 80 billion years. Larger stars consume their fuel faster than smaller stars, so this result makes sense.