The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen

Question

The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.

Part A

The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.

Express your answer using two significant figures.

Part B

Given that our solar system is now about 4.5 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?

Express your answer using two significant figures.

Explanation / Answer

(A) Total mass of the Sun = 2×10^30 kg

Mass of hydrogen in Sun =  2×10^30 *0.76 kg

Mass of hydrogen ever available for fusion = 2×10^30 *0.76 *0.12 kg = 1.824*10^29.

Mass of hydrogen fuses each second = 600 billion kg/second.

Time hydrogen will last in seconds= 600 billion kg = 1.824*10^29/seconds.

= 0.00304* 10^29 = 3.04* 10^17.

Time hydrogen will last in seconds = 1 year = 31,536,000 seconds.

  31,536,000 * x = 3.04* 10^17 = 9.6 billion years.

(B) Present age of sun = 9.6-4.5 billion years

Time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.

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