Answer to Question #280903 in Astronomy | Astrophysics for Cat.G

Question

How long is a 6.8 solar mass star expected to live? (Give your answer in years, just the number, no need to include the unit.)

Answer 1

The life expectancy of the star (assume it belongs to main sequence) is given as follows (see https://astronomy.swin.edu.au/cosmos/m/main+sequence+lifetime):

$$t \approx t_S\left(\dfrac{M}{M_S} \right)^{-2.5}$$

where $t_S = 10^{10}years$ is the life expectancy of the Sun, $M_S$ is the mass of the Sun. If $M = 6.8M_S$ is the mass of the star, obtain:

$$t \approx10^{10}\cdot \left(\dfrac{6.8M_S}{M_S} \right)^{-2.5} \approx 83\times 10^6years$$

Answer. 83 million years.