by John Church
Fear no more the heat o’ the sun,
Nor the furious winter’s rages.
– Cymbeline, Act IV
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 and classic introduction to astronomy by Kelvin McKready. My father brought it home from the Virginia State Library when I was about ten. I devoured every page, although many of the technical details were way over my head. This book was largely responsible for my lifelong interest in astronomy, some bits of which I have written about elsewhere. When I left Richmond after finishing college, the book stayed in my parents’ home, having been discarded by the library. My father gave it to me, and I have it still.
McKready’s excellent exposition was interspersed with astronomy-related poetical selections from Victorians such as Matthew Arnold and Alfred Tennyson. A sample of the latter will suffice:
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 …
A ten-year-old boy cared little for the maudlin sentimentality of Maud (he might, later on), but he was greatly impressed by such imagery. For he himself had seen Auriga and the Heavenly Twins keeping vigil above the place where the Giant Hunter rested of a delicious late April Richmond evening. And he had shared the thrill of chill November twilights such as those watched by the narrator of Locksley Hall:
Many a night I saw the Pleiads, rising thro’ 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 all take for granted: rising early in the morning to send us off to school or work, then setting in the evening as we reflect on the day and prepare for dinner. It can get in our eyes during our morning or evening commutes in 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 thing that heats the earth and keeps it 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 ridiculously tiny speck, no bigger than a gnat would appear from several yards away. The earth catches only one part in two billion, two hundred million of the total energy that the sun pours out into space. Put another way, the sun could light up and power well over two billion earths at once. Imagine the amount of energy that the total daylit side of 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, 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 enormous thing.
Scientists sometimes entertain themselves by doing approximate calculations in their heads. (Yes, aren’t we such jolly people?) Lying in bed once, I was curious as to about how much of the sun’s surface would be required to take care of the entire earth’s solar energy budget. As we learned in elementary geometry, the surface area of a sphere is four times pi times the square of the sphere’s radius. Astronomy buffs know, or ought to know, that the sun’s radius is 432,000 miles, or 4.32 times 10 to the 5th power (expressed this way for ease in handling such large numbers). Square this in your head and you will have roughly 20 times 10 to the 10th power. And four times pi is about 12. So the area of the sun’s surface must be about 240 times 10 to the 10th power square miles; simplify this to 2.4 times 10 to the 12th power. In other words, 2.4 trillion square miles.
Now we already know that the sun can light up 2.2 billion earths, as McKready told us. Therefore, it would take only about eleven hundred square miles of the sun’s surface to give full daylight and heat to the entire sunlit side of the earth. Now eleven hundred square miles is not really very much; it’s about the size of two average counties in the small state of New Jersey where I live. So the sun must be incredibly hot and bright. Well, any fool knew that without doing the calculation, but it did help put me to sleep.
Deep inside the sun, five million tons of matter are being tortured to death every second in nuclear reactions and converted to energy 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 it slowly loses mass – the rate is about one earth equivalent per 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 and melting it completely. 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. I couldn’t figure these out in my head the other night because I was already bored to death and sound asleep (see, this technique works). The total power being continually released by the sun is about 5 times 10 to the 23rd power horsepower. A number of this size is especially interesting to chemists, because it’s close to what’s known as “Avogadro’s number.” This latter number, about 6 times 10 to the 23rd power, 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 as we already know. Hydrogen has an atomic weight of very close to 1 (convenient, since it’s the lightest element), and oxygen is 16. So the molecular weight of water is 18 (18.02 if you want to get technical). Now a mole of any compound is defined as the number of grams of that compound numerically equal to its molecular weight. So a mole of water has a mass of 18.02 grams. Volumewise, this is between three and four teaspoonfuls of water. This small swallow has more molecules in it than the horsepower of the sun! Hard to believe, but true.
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 conventional light bulb. This is the power output of a little under two square millimeters of the sun’s surface. If you do the math, to power all the seven billion people on earth would theoretically require a piece of the sun only about the size of the playing surface at a baseball stadium.
Play ball! But please put on some sunscreen.