Astronomy is even more beautiful by the numbers
Astronomy is a richer experience if you stop and contemplate the numbers. But cosmic distances, sizes, and other properties are mind-numbingly large. Our Sun’s mass is equivalent to four million trillion trillion pounds and it has a luminosity of 400 trillion trillion Watts. How can we get our heads around quantities like these?
It’s tempting to just enjoy the pretty pictures and accept that the universe is huge and descriptions require mind-boggling numbers. Nothing wrong with that, but those very numbers and the quantities they represent help inspire gut-level confidence in astronomical ideas and understanding. Fully appreciating the vastness of the physical universe, of stars and galaxies and the rest, enriches the experience of those pretty pictures. As one of my college professors was fond of saying, “We need to get these concepts behind our belly buttons!” A fun and effective way to digest astronomical quantities is to play a game called Numerical Analogy™.
The rules of the game are simple: recast those numbers into contexts that we experience in our daily lives. You don’t have to wait for someone to create numerical analogies for you, but it helps to have a few starting points at your fingertips.
Here we go. The current estimate of the number of galaxies observable in our universe is several trillion. How big is a trillion? Large countries have budgets in the trillions of dollars, but for me that’s not helpful.
Numerical Analogy round one. A book containing a million characters of single-spaced text would be about 300 pages long, depending on font and page sizes, and it would occupy a million bytes (1 Megabyte, MB) of uncompressed device memory. For a billion characters we need 300,000 pages or a thousand 300-page books and a Gigabyte (GB) of storage. A trillion characters would fill a million such books — about the number of volumes in a medium-sized metropolitan library — or a Terabyte (TB) of computer memory. And that’s just plain text, no images.
Round two. Start from the number one and count up 1, 2, 3…one number per second:
- Counting to a million seconds will take you 278 hours or 11.6 days (call it 12 days).
- A year is 31.5 million seconds long, roughly pi times ten million seconds.
- A billion seconds is 11,600 days so it will take 32 years to count to a billion at this rate.
- To reach a trillion seconds you will need to enlist your descendants. At one trillion seconds they will have been counting for 32,000 years.
Those numbers aren’t really very big but hold on to your stop watch. The Andromeda galaxy is 20 million trillion miles from the Milky Way.
A quick note on writing out numbers and units of measure: I’m deliberately writing numbers out and not using scientific notation, also known as powers of ten notation. Powers of ten notation is a great shorthand for large numbers, but writing them out requires a pause to contemplate the quantities more fully than the shorthand. So the distance is 20 million trillion miles rather than the equivalent 2.0x10¹⁹ miles. And I’m writing from the United States where we use inches, feet, miles, ounces, pounds, gallons, and the Fahrenheit temperature scale. Americans, can we please just graduate to the metric system? We can do powers of ten! We do it with money every day. If you are reading from a country that already uses the metric system please give us some encouragement and support to make the change. Meanwhile, as we’ll see shortly, in astronomy it often doesn’t matter what system we use.
Back to the Andromeda galaxy. How big is a million trillion? It’s officially a quintillion, but I like “million trillion” better. Somehow it’s easier for me to imagine that way. It’s also a lot more fun to say. Sometimes the numerical analogy can be as simple as applying the big number in a more familiar context closer to home. For instance, depending your elevation above sea level, there are about 400 million trillion air molecules in a cubic inch of the air you are breathing. How big is a trillion trillion? There are a few trillion trillion H₂O molecules in a glass of water.
Round three. Returning to our crib sheet of facts to use in playing the Numerical Analogies game:
- The international space station orbits just over 250 miles above the Earth’s surface.
- The diameter of Earth is just under 8,000 miles.
- The Earth-moon distance is about 250,000 miles.
- The Earth-Sun distance is about 93 million miles.
- The planet Neptune is about 3 billion miles from the sun.
- Our solar system is about 24 trillion miles in diameter out to the most distant orbits of comets in the Oort Cloud.
While we’re on the subject of our solar system, once we leave it our choice of physical units (metric or not) quickly becomes almost irrelevant. Quantities get so large that it doesn’t matter if you use miles or kilometers, miles per second or kilometers per second, or in some cases even Celsius, Kelvin, or Fahrenheit. The numbers are just big. Our human- and planet-sized measurement systems begin to fail us utterly.
But failure is an opportunity to try a different approach, right? So one way astronomers measure and describe distance is to use time units. You probably do this, too. How far is it from my home town to New York City? About four hours depending on traffic and how fast I drive. When traveling I usually care more about how long my trip will take than how far I have to go unless I’m on my bicycle. Astronomers do this all the time but we ask a slightly different question: How long would it take light to travel this distance? Since most astronomical observations collect light of one form or another it’s useful to describe distances in light travel time. At 186,000 miles per second, the distance light travels in one year is 6 trillion miles or — you guessed it, I bet — one light year.
Now the numbers get much more manageable. Our solar system is about four light years across and the closest star to our Sun is just over four light years away so when you get to the edge of the Oort Cloud you only have two light years to go to arrive at Proxima Centauri. The Milky Way galaxy is about 100,000 light years across; it’s actually 200,000 light years across if you include its dark matter halo and the outermost stars in their far-flung orbits. The Andromeda galaxy is 2.5 million light years from us here in the Milky Way galaxy. Beyond the closest galaxies even distances in light years start to require huge numbers. We need tens of billions of light years to locate the most distant observable galaxies.
You’ve got the hang of this so for our final round we’ll pick up the pace and make use of our crib sheet of numerical analogies. Distances aren’t the only things we want to know.
Density. The average density of hydrogen gas in the universe when it was just a few hundred thousand years old was apparently a few thousand atoms per cubic inch. This is a very high density compared to the current average value in interstellar space, which is about one atom per cubic inch. It’s a vanishingly low density environment compared to our everyday experience here on Earth, though. Recall that the air you are breathing as you read these words has a density of 400 million trillion molecules per cubic inch. The best vacuum ever created in a laboratory contains a hundred thousand molecules per cubic inch; 100,000 times the hydrogen gas density in the space between stars in our galaxy. Kind of gives ‘the vacuum of outer space’ a whole new meaning.
Temperature. The core temperature of the sun is 15 million on the Kelvin scale. This is also 15 million degrees on the Celsius scale; well, actually, it's 14,999,727 C. On the Fahrenheit scale that’s 27,000,000 F. This is why I think it’s perfectly fine to say that the core temperature of the sun is tens of millions of degrees, full stop. It’s wicked hot using any temperature scale.
Luminosity is energy per second (power) emitted in all directions from a glowing source like a star or a light bulb. We often measure power, and therefore luminosity, in Watts. The sun has a luminosity of 4 hundred trillion trillion Watts. If we could capture all of that sunlight we could power a four trillion trillion 100-Watt lightbulbs.
Speed. Standing on the spinning Earth’s equator you are moving at about 1000 miles per hour. The Earth is orbiting the sun at 70 thousand miles per hour and the sun is orbiting in the Milky Way galaxy at around 500 thousand miles per hour. Located 26 thousand light years from the Milky Way center, the sun completes a Milky Way orbit in 230 million years. So the last time the sun was in its current orbital position in the Milky Way was before the dinosaurs lived here on Earth.
Age. The universe is 13.8 billion years old. Planet Earth is 4.6 billion years old. Sometimes a numerical analogy and the associated insight can be as simple as a proportion: our universe is only three times older than our planet! I say “only” because the first time I really stopped and contemplated these quantities, which I had known for decades by the way, I was astonished. Our planet has been around for a really long time.
The richness of our knowledge of the universe, which of course is much larger than us, depends upon the richness of our understanding of atoms and subatomic particles, which are much smaller than us. Determining and really appreciating the physical properties of matter in this range of scales is an essential part of knowing the universe: all matter, energy, space, and time.
