by John A. Church
Whenever I have trouble getting to sleep, which sometimes happens to people as they get older, I just think about the sun.
I first learned interesting things about the sun from The Beginner’s Star-Book. a delightful introduction to astronomy by Kelvin McKready that I read when I was about twelve. McKready’s excellent exposition was replete with astronomy-related selections from Victorian poets such as Matthew Arnold and Alfred Tennyson. A sample of the latter will surely be more than enough:
My mood is changed, for it fell at a time of year
When the face of the night is fair on the dewy downs,
And the shining daffodil dies, and the Charioteer
And starry Gemini hand like glorious crowns
O’er Orion’s grave low down in the west . . .
This young lad was impressed by such imagery. For he had also seen Auriga and the Heavenly Twins keeping vigil above the place where the Giant Hunter rested on a delicious late April evening. And he had known the thrill of chill November twilights such as those watched by the narrator of “Locksley Hall”:
Many a night I saw the Pleiads, rising through the mellow shade,
Glitter like a swarm of fireflies tangled in a silver braid.
There was a chapter in McKready’s book describing the sun. Now the sun is something we take for granted: it rises early in the morning to send us off to school or work, then sets in the evening as we reflect on the day and prepare for dinner. It can get in our eyes during our commutes in the wintertime, might burn us in the summer, and doesn’t always shine when we most want it to. Reading McKready, however, gives us a little more respect for this monstrous object that heats the earth and keeps it safely in its orbit.
Anthropocentric conceit would have us imagine that the sun exists for our benefit alone, but some elementary facts disabuse us of this notion. As seen from the sun, the earth is nothing but a tiny speck. It catches only one part in 2,200,000,000 of the total energy that the sun pours out into space. To put it another way, the sun could light up and power well over two billion earths at once. Imagine the inconceivable amount of energy that the total daylit side of the earth is receiving at any one instant, multiply it by this factor, and you will have some remote idea of the sun’s power. And it has been doing this for billions of years and will continue to do so for billions more. (Peace, spirit of Carl Sagan, I didn’t mean to overuse your proprietary word.)
Well over a million earths could fit inside the sun’s globe. If the earth were at its center, the moon in its orbit would be only a little more than halfway out to the sun’s surface. What an impressive thing we have here, and we don’t even have to pay for it. (Imagine if we did.)
Scientists, strange people that we are, sometimes entertain ourselves by doing approximate calculations in our heads. Lying in bed one night, I was curious as to about how much of the sun’s surface would be required to take care of the earth’s entire solar energy budget. As we learned in elementary geometry, the surface area of a sphere is four times π times the square of the sphere’s radius. Astronomy buffs know, or ought to know, that the sun’s radius is 4.32 x 105 miles. Square this in your head and you have roughly 20 x 1010 square miles. And four times pi is about 12.5. So the area of the sun’s surface must be about 2.5 x 1012 square miles, or in other words, 2.5 trillion square miles of blazingly hot plasma. Now we already know that the sun could light up 2.2 billion earths, as McKready told us. Therefore, it would take only about 1,100 square miles of the sun’s surface to give full daylight and heat to the entire sunlit side of the earth. This is only about the size of two average New Jersey counties.
Deep inside the sun, millions of tons of matter are being converted into energy every second by the enormous gravitational pressure of the overlying material. The sun would really like to explode from all this released energy, but it can’t because of this same gravitational confinement, and everything stays almost perfectly in balance. As the sun slowly loses mass – the rate is about one earth equivalent every 40 million years – it continually expands at a very slow rate, partly because of decreased gravity, but mostly because its power output gradually increases due to complicated changes in its mode of energy generation. After many billions of years it will become a “red giant,” swelling to about the size of the earth’s orbit; talk about global warming! Long before things get to this stage, we shall have had to move; it’s not too early to begin thinking about it.
Now for some more illuminating facts. The total power generated by the sun is something like 5 x 1023 horsepower. A number of this size is especially interesting to chemists, because it’s in the same ballpark as “Avogadro’s number,” which is about 6 x 1023. This is the number of molecules in what’s called a “gram-molecule” (also known as a “mole”) of any chemical compound. Take water as an example, made of two hydrogen atoms and one oxygen. Hydrogen has an atomic mass of about 1 (convenient, since it’s the lightest element), and oxygen’s atomic mass is 16. So the molecular mass of water is about 18. Now a mole of any compound is defined as the number of grams of that compound numerically equal to its molecular mass, so a mole of water has a mass of about 18 grams. This is between three and four teaspoonfuls of water. This small swallow has more molecules in it than the horsepower of the sun! But, like Rodney Dangerfield, we chemists don’t get no respect for telling people how small a molecule is.
One more factoid for insomniacs and I’m done. How much of the sun’s surface do I personally need to keep me alive? An average person’s metabolic power consumption is about a hundred watts, or like one bright light bulb. This is the power output of a bit of the sun’s surface about the size of a pinhead. So now I finally know my place in the grand scheme of things.
Amateur Astronomers Association of Princeton 