Let us assume that the core of the Sun has one-eighth the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius. We assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. We also assume that the Sun continues to burn hydrogen at the rate of . We have to find the time in which the hydrogen in the Sun’s core will be entirely consumed. The Sun’s mass is .

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We assume that the core of the Sun has one-eighth the Sun’s mass. The mass of the Sun is . Therefore, the mass of the Sun’s core will be

We assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. Therefore, the mass of hydrogen in the core of the sun will be

We also assume that the Sun continues to burn hydrogen at the rate of . Therefore, the time in which the hydrogen in the Sun’s core will be completely consumed will be