Answer to Question #104716 in Astronomy | Astrophysics for Nikhil

Question

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

Answer 1

The dependence of the fuel burn performed by stars and their mass is not as straightforward as we would expect. It depends on what exactly the mass of the star relative to the Sun is:

$$T_\text{Star}=\frac{T_☉}{(M_\text{Star}/M_☉)^{p-1}}$$

For stars with a mass lower than 10 solar masses, the value of $p$ in the equation above is 4, for stars heavier than 30 solar masses $p=3$.

Therefore, the lifetime will be

$$T=\frac{10^{10}}{(5)^{4-1}}=8\cdot10^7\text{ years}.$$