Watt, How Much Energy is There?

We talk A LOT about energy in almost every physics course all the way through grad school. Like a lot a lot. It takes 24 joules (J) of work to move the block up the 30-degree incline. The energy of a single green photon is 3.8 x 10-19 J. An electron with a de Broglie wavelength of 1 angstrom (Å) has 2.41 x 10-17 J of energy. Energy considerations and limitations are everywhere in physics and astronomy.

It turns out that’s because energy is one of the seven fundamental units. The SI system of units outlines seven base units: kilogram (kg) for mass, meter (m) for length, seconds (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. Most other measurements are in derived units, meaning they are just combinations of these bases. For example, velocity uses length (m) and time (s). Force uses both of those and mass (kg).

Okay, but how much energy is out there to use? That’s kind of a hard question to frame, but to phrase it a different way, If we wanted to generate as much energy as possible, what could we use and how would we do it?

Years ago a very famous physicist (and big fan of SPS) was inspired by a science fiction book by Olaf Stapledon called Star Maker to explore this concept—a civilization needing to generate as much energy as possible—and in 1960, published a paper in the journal Science titled “Search for Artificial Stellar Sources of Infrared Radiation” about this very idea. You can read the paper or hear about it directly from him in a video (check out the links in the sidebar), but in summary, he imagined a civilization capturing as much of the energy produced by a star as possible. The remaining infrared signature of such stars could be detectable, as it would be matched to intelligent life activities.

And, in his words, “The science fiction writers . . . imagined [the energy capturing device] then to be a spherical rigid object, and the aliens would be living on [or in] some kind of artificial shell—a rigid structure surrounding a star.”

That “wasn’t exactly what I had in mind,” continued the paper’s author, Freeman Dyson. “But in any case, that’s become then a favorite object of science fiction writers. They call it the ‘Dyson sphere,’ which was a name I don’t altogether approve of. But anyway . . . I’m stuck with it. But the idea was a good one.”

This concept is the foundation for this issue’s puzzler!

lf we were to create a Dyson sphere, how much energy could it generate?

There are lots of different ways you could estimate this. The important parts are to use a method that makes sense to you that is based on values or estimates that you remember or are comfortable with.

Here’s the outline of one method. I challenge you to use a totally different method and see how they compare. I’ll even give some suggestions for alternate methods at the very end.

STEP 1: DEFINE YOUR PROCESS

One fact that I will always remember from my solar physics courses is that the average solar radiation reaching Earth’s atmosphere is about 1361 W/m2, and at sea level we get about 1000 W/m2. Remember that a Watt (W) is defined as a J/s, which is energy per unit time.

Imagine a surface around the sun located at the same distance Earth is, also known as 1 astronomical unit (AU). If we were to capture all of that energy flux, we’d have a really good estimate for our Dyson sphere. (To actually capture it, we could build solar cells and thermoelectric generators, also called Seebeck generators.) So our process is to figure out the solar radiation flux and surface area of our Dyson sphere.

STEP 2: DRAW A PICTURE

In Fig. 1 we can see that Earth is about eight light minutes away from the sun. (Fun fact: If the sun turned off, it would be eight minutes before it looked dark to us.)

STEP 3: DO THE MATH

Putting this information together, as shown in Fig. 2, gives us a value of roughly 1026 J/s or 1034 J/year (since there are about π x 107 minutes in a year). That’s huge! For context, the world currently uses around 1 ZJ of energy per year. Z here is for Zeta or 1021.

Now it’s your turn! l encourage you to find a different way of estimating the energy a Dyson sphere could generate or, if you are the curious type, how much mass would it take to make this hypothetical Dyson sphere. Happy calculating!

BONUS!

My mentor, Professor John Andersen, once shared a few fortuitous relations he always kept in the back of his head. I am happy to share these with you:

• The sun is eight light minutes away from Earth (that estimate is about 5 percent too small).
• The moon is one light second away (about 25% too small).
• The sun and moon have the same angular size to us, which is about 0.5 degrees (about 5% too small).
• Combining the above facts, you can determine the lunar and solar diameters.
• Earth is 81 or 34 times more massive than the moon.
• The sun is 333,000 times more massive than Earth.