Sunday, March 27, 2011

A Sun Made Out Of Bananas

I was cruising the information superhighway today, and came across some random article about neat science facts.  I usually treat these with quite a bit of skepticism, as they generally take a single basic fact and ignore everything else in order to derive something which is "neat".  This one didn't disappoint.  The first fact caught my eye:
If the Sun were made of bananas, it would be just as hot

The Sun is hot, as the more astute of you will have noticed. It is hot because its enormous weight – about a billion billion billion tons – creates vast gravity, putting its core under colossal pressure. Just as a bicycle pump gets warm when you pump it, the pressure increases the temperature. Enormous pressure leads to enormous temperature.

If, instead of hydrogen, you got a billion billion billion tons of bananas and hung it in space, it would create just as much pressure, and therefore just as high a temperature. So it would make very little difference to the heat whether you made the Sun out of hydrogen, or bananas, or patio furniture.
As I said above, this has a nugget of truth, i.e., massive objects will compress themselves and increase in temperature.  There is no doubt about this, indeed much of the Earth's heat is left over from it coalescing and the residual effects.  However, it ignored the fact that the heat would quickly (in astronomical time scales) dissipate and the object would cool down.  Nuclear fusion is what sustains a star's heat for billions of years.

Luckily my fellow pedantic internet nerds corrected this oversight and the following was added:
Edit: this might be a little confusing. The heat caused by the internal pressure would be similar to that of our Sun. However, if it's not made of hydrogen, the fusion reaction that keeps it going wouldn't get under way: so a banana Sun would rapidly cool down from its initial heat rather than burning for billions of years. Thanks to people who pointed this out.
That being said, I felt the desire to go one step further in my pedantry.  I knew bananas are mostly water, which is mostly hydrogen.  I wondered if the sun would be able to undergo fusion if it were made out of bananas.

Thanks to the wonders of the internet I knew within seconds that a banana is about 70% water and 30% carbohydrates.  I'm going to assume the peel is about the same in makeup as the insides (or that our banana sun would be peeled).  We all know that water is H2O, but what are carbohydrates?  I looked up which carbohydrates are in a banana, and then looked up what those carbohydrates are made of.  If I knew anything about organic chemistry, I would have known that they all have roughly the same ratio of 1 C : 2 H : 1 O.  Now that I knew the chemical ratios I had to figure out what the ratios were by mass.  Hydrogen has a mass of about 1 amu, carbon 12 amu, and oxygen 16 amu.  Which means that water is 11.1% hydrogen by mass, 88.9% oxygen.  Carbohydrates are 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen, by mass.

By the powers of math, we find that the final make up of our banana sun would be 9.78% H, 78.22% O, 12.00% C.  Oxygen and carbon can fuse, but our sun isn't massive enough to make it happen.  So only the 10% hydrogen could fuse.  In addition, the oxygen and carbon would settle in the core possibly preventing hydrogen fusion in the outer layers.  I don't know enough about stellar evolution to say for sure what the result would be.  But, I'd guess that today we'd have something pretty similar to a white dwarf.

While the banana sun would likely be rather bright today, and still qualify as a star, it is unlikely that it would have given off enough heat for life to form on Earth.  I suppose you should thank your lucky stars that a sea of free electrons and protons will form hydrogen atoms and not bananas (well at least not for a very long time).

As an epilogue I'll answer how many bananas one would need to equal the Sun's mass.  Google tells us that a single banana is 125 grams, and Google's wonderful calculator makes short work of the calculation:
1.6 x 1031 or 16,000,000,000,000,000,000,000,000,000,000 bananas.  You're gonna need a bigger boat.