Question

How long will a 5MΘ star burn hydrogen as fuel, given that the Sun will do so for
about 1010 years?

Answer 1

Answer on question #61095, Physics / Astronomy | Astrophysics

How long will a 5MΘ star burn hydrogen as fuel, given that the Sun will do so for about $10^{10}$ years?

**Solution:**

The dependence of the lifetime on the star mass:

$$t = t _ {\Theta} \times \left(\frac {M}{M _ {\Theta}}\right) ^ {- 3}$$

For the star with $M = 5M_{\odot}$.

For the sun $t_{\Theta} = 10^{10}$ years.

The final expression:

$$t = 10^{10} \text{ years} \times \left(\frac {5 M _ {\Theta}}{M _ {\Theta}}\right) ^ {- 3} = 10^{10} \times 5 ^ {- 3} = 8 \cdot 10^{7} \text{ years}$$

Answer: the star will burn its fuel in $8 \cdot 10^{7}$ years

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