The total mass of the Sun is about 2 ×1030 kg, of which about 75% was hydrogen when the Sun formed. Only about 11% of this hydrogen ever becomes available for fusion in the core (the rest is in the layers of the Sun where the temperature is too low for fusion).
a. Calculate the total mass Astrof hydrogen available for fusion over the lifetime of the Sun
b. The Sun radiates 4 × 1026 joules per second (= watts). How much of the Sun's hydrogen (in kg) is converted to energy each second? How long will the Suns initial supply of available hydrogen last, in years? (c=3 ×108 m/sec, and 1 year = 3.16 ×107 seconds).
c. Given that our Solar System is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?