Question

The estimated life time of the sun on mainsequence is ~10^10 yrs. Determine the mainsequence life time of a star of 0.5 Mo.

Answer 1

If you make a rough estimate of how much energy the sun emits, you’ll get something like:

$$E=0.007 \times 0.1 \times M_{sun}c^2$$

the rate at which the sun is giving off energy is equal $3.8 \times 10^{26} W$ . And lifetime of the sun is

$$t_{sun} = \frac{E}{3.8 \times 10^{26}} = \frac{0.007 \times 0.1 \times M_{sun}c^2}{3.8 \times 10^{26}}$$

If mass of the star is $M_{star} = 0.5M_{sun}$, then

$$t_{star}=0.5t_{sun} = 5\times 10^9 yrs$$