The total mass of the Sun is about 2 × 1030 kg, of which about 75% 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.
a) Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun. Express your answer using two significant figures.
b) 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.
c) Express your answer using two significant figures.
d) 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.