Feb 162012

I always find these numbers astonishing.

The solar constant, the amount of energy received by a 1 square meter surface at 1 astronomical unit (AU) from the Sun is roughly s = 1.37 kW/m2. Given that 1 AU is approximately 150 million kilometers, or r = 1.5 × 1011 m, the surface area of a 1 AU sphere surrounding the Sun would be A = 4πr2 = 2.8 × 1023 m2. Multiplied by the solar constant, we get P = sA = 3.9 × 1026 W, or the energy E = sA = 3.9 × 1026 J every second. Using Einstein’s infamous mass-energy formula E = mc2, where c = 3 × 108 m/s, we can easily calculate how much mass is converted into energy: m = E/c2 = 4.3 × 109 kg. Close to four and a half million tons.

The dominant fusion process in the Sun is the proton-proton chain reaction, in which approximately 0.7% of the total mass of hydrogen is converted into energy. Thus 4.3 million tons of pure energy is equivalent to over 600 millon tons of hydrogen fuel burned every second. (For comparison, the largest ever nuclear device, the Soviet Tsar Bomba, burned no more than a few hundred kilograms of hydrogen to produce a 50 megaton explosion.)

Fortunately, there is plenty where that came from. The total mass of the Sun is 2 × 1030 kg, so if the Sun was made entirely of hydrogen, it could burn for 100 billion years before running out of fuel. Now the Sun is not made entirely of hydrogen, and the fusion reaction slows down and eventually stops long before all the hydrogen is consumed, but we still have a few billion years of useful life left in our middle-aged star. A much bigger (pun intended) problem is that as our Sun ages, it will grow in size; in a mere billion years, the Earth may well become uninhabitable as a result, with the oceans boiling away. I wonder if it’s too early to start worrying about it just yet.

 Posted by at 12:24 pm