May 21, 2015


Lately I find myself thinking a lot about deep time—about thousands and millions and hundreds of millions and billions of years. In discussions of astronomy and geology we toss around those lines of zeros about as casually as we talk about what we had for dinner the night before. I had a Thai-chicken stir-fry, dinosaurs died off 65,000,000 years ago, and the universe is 13,800,000,000 years old…give or take 100,000,000. We’re so used to hearing these big numbers that we don’t really consider what it is that all those zeros stand for, and we forget just how big they are.

Even when we try, it’s really hard for creatures that live only a few decades to even begin to conceptualize what one billion years, or even one thousand years, feels like. So when we think about certain places and events—the carving of the Grand Canyon, the formation of the solar system, the evolution of life—we tend to scratch our heads in disbelief. Rock is hard, how could flowing water carve through a vertical mile of solid rock in only a few million years? Everything in space is so still, how could it be that in just 5 billion years a bunch of gas and dust condensed, swirled, banged around, and then, voila, we have the sun and all the planets? Humans are humans. How could I evolve from something that looked like a fish, or even an ape? Little changes happen, for sure. Maybe some people are taller or shorter, or you inherit your grandfather’s nose, or your mother’s broad shoulders…there’s variation and change, but not enough, and certainly not enough time to transform an amoeba into a walking, talking, thinking human being…is there?

But yes, actually, there’s been plenty of time for all of these things to occur. And the teensy-tiny almost unobservable changes that will become the next epoch’s marvels are happening all around us today. So as I’ve been thinking about deep time, I’ve also started looking for these smaller more human-scale occurrences that can help me account for the passage of years and get a sense for the kind of time that’s wrapped up inside all those zeros.

Yesterday I got into precession.

I learned about precession soon after I got into amateur astronomy several years ago. Someone in SLAS was giving a constellation tour and said that Polaris—the ever-constant North Star, the one little starry beacon that stays put while everything else spins around it—had not always been the North Star. !!!WHAT!!! And not only that, but in another two thousand years, the north star will be Gamma Cephei…some random star in this totally different constellation that I’d never even heard of. My mind was blown.

Our Earth spins on an axis once every 23 hours and 56 minutes. The tilt of that axis is what gives us the seasons, and those lost 4 minutes per spin are what makes the constellations appear to rise and set 4 minutes earlier than they did the day before. Because the Earth is not perfectly round and is constantly tugged on by the sun and the moon, it also wobbles as it spins. Earth is often compared to a spinning top that traces out little circles as it moves across a tabletop. And here I’m always reminded of Leonardo DiCaprio’s character in Inception: the totem he used to tell him whether or not he was dreaming was a little top. If he set it to spin and it wobbled, the world around him was behaving normally, and he knew he was awake. If it didn’t…he was still trapped in a dream world…the dramatic music would go up a notch and we’d all grip our seats a little tighter.

Wobbling is natural. And Earth’s wobble is called precession. As the Earth spins day after day, year after year, century after century, its axis traces out a slow circle across the sky. It takes about 26,000 years for Earth to trace a complete circle and it is purely by chance that at this point in history, our axis happens to be pointing near the 45th brightest star in the sky: Polaris.

26,000 years is a long time to trace a circle, but there’s still enough movement over a short enough period of time that precession has been observed and documented by individual human observers. Yesterday, I wondered if I could find a way to observe it myself. First I wanted to figure out how much the pole should be expected to shift in one year. If the observed change is, say, only an arc second—about the width of a human hair seen from 10 meters away—then forget it…there’s no way I could get that kind of precision with the tools I’ve got on hand*.

*My tools: ruler, pink protractor, bic pens, string, duct tape…you get the idea.

To figure this out, we know there are 360 degrees in a circle, and that it takes 26,000 years to trace them all out. That means there’s a movement of about .014 degrees per year. What does that mean visually? Well, the full moon takes up about .5 degrees in the sky, so we can already see it’s quite a bit smaller than that. How much smaller? Well, there are 60 arc minutes in a degree, and 60 arc seconds in an arc minute. So multiplying our yearly progress of .014 degrees by 60 gives us .84 arc minutes traced per year. Multiply that by 60 and we now have about 50 arc seconds traced per year. 50 arc seconds is about the diameter of Jupiter as seen from Earth…or a little less than the thickness of typical birthday-card stock held at arm’s length. That’s pretty small. But it’s something—especially if my dad keeps sending me birthday cards every year! All those little layers are going to add up.

Now imagine if I had a little more than a century’s worth of precession to work with. That’s more than a typical human lifetime, but it’s still a time span most of us can relate to. At the dawn of the 20th century, there were 1.6 billion people living on Earth, America had only 45 states, automobiles had been around for a decade or so, and the Wright brothers had just made their first flight. It was a pretty different world, but my great grandparents—some of whom I was able to know as a child—would have been kids around that time.

I remember being a kid, and I’ve seen movies of my parents as kids, and my grandparents as young adults. As I age, I understand more and more how time can slip away. One moment you’re in grade school playing on the swings at recess—you think, “I’ll never be old enough to…” drive, or date, or fill in the blank with whatever grown-up dream occupies your fancy. And then suddenly you’re in high school…and then it’s your 10 year high-school reunion…and you’re working and paying bills and dreaming about all those just-yesterdays at recess. You can think of a century as being about three or four generations.  And though technology has advanced rapidly in the last century, I imagine that the experience of living an individual life still feels similar. So, what did the North Star look like to my great-grandparents when they were children? And how does it compare to where I see it today? I decided to Google that…and this is what I found.

A photo published in 1902 of star trails centered on the North Pole, featured in an article by George Ellery Hale.

Another quick Google search yielded numerous spectacular star-trail images from more recent years, including this one from 2012.

It took me quite a while (and a good number of accelerated polar spins in Stellarium) to figure out which stars were which in each image, and was a lot harder than I thought it would be. They both use different exposure lengths, are taken at different times of the night (and probably different seasons of the year), one is color (helpful for figuring out stars), one is not (not helpful for figuring out stars), and both have their own visual idiosyncrasies that conspired to fool my eyes. I finally inverted the colors, which seemed to help, and after enough comparison I was finally able to nail down a few stars.

I used a protractor to find each circle’s center, which marks the location of the true North Pole in each photo. Looking back and forth between the two images, though they’re at slightly different scales, I thought I could see a pretty clear difference in the pole’s location relative to Polaris and the other stars.

But to be sure my eyes weren’t deceiving me, I made a triangle between the same two stars and the North Pole as they appear in both images and measured their angles to see how they'd changed in 110 years.



Though I can’t measure the actual number of degrees the pole moved from the limited information I have in the photos, they do very clearly show that the pole is moving. In fact, In 110 years, the pole has moved about 1.5 degrees closer to Polaris—the diameter of 3 full moons—and it will be as close to Polaris as it can get—a little less than one full moon away—in the year 2100.

Now, I’m not an astronomer and I’m not a mathematician, so to the pros, my little observation here might seem trivial. A real astronomer could do much more calculation than I can muster, but I’ll be honest, I was pretty excited when my measurements showed something!

Try to picture it: in about 200 years, the North Pole changes by about the diameter of 4 full moons. I wasn’t around in 1900 to begin the period of observation I’m focusing on here, but my great-grandparents were. I won’t be around in 2100 to see Polaris make its closest northern approach, but my sister’s kids—one of whom will just be starting kindergarten next fall—just might. By that time, they might even have their own grandkids. That would make me the legendary crazy great-grandaunt (is there such a thing?) that was alive at the turn of the 21st century. So in 200 years—and about 8 generations—there’s a chain of acquaintance and memory (and, yes, these days we also have photos), that bears witness to an observable change in a celestial point that I grew up believing is constant and unchanging.

Now think about this:

In the amount of time that it took for Earth to complete its last full precession:

9,490,000 sunrises warmed the Atlantic coast (though only about 3,600,000 occurred over the eastern shore of Lake Michigan…it only arrived on the scene 10,000 years ago).

26,000 winters melted into spring.

10,400 generations passed on their memories, and humanity advanced from making its first clay pots and fibrous baskets, to sending mobile science laboratories to the surface of Mars.

The rim of what would become Bryce Canyon National Park receded about 6500 feet.

and the Himalayas rose by 1 mile.

And on into the future…

Polaris will precess back into its current position 3,800 more times before Amasia—the next great supercontinent—will form.

9,600 more precessions will occur as the sun makes its next trip around the core of the Milky Way Galaxy.

We’ll get to complete an additional 192,000 precessions before our sun swells into a red giant with a diameter of Earth’s current orbit…and any life that remains on Earth is toast.

And again, my mind is blown.


  1. MY mind is blown!!! You have a great gift for teaching. I would take a class from you. It's so interesting to explore these ideas and look from different perspectives at the universe we occupy. Maybe we can change misconceptions and progress to the next evolutionary level

  2. Kelly, This entry is really magnificent and inspired nature and science writing. You've outdone yourself and should be proud. - Kurt, SLC, UT.

  3. Kelly,
    This is a wonderful post; I like the way you are linking deep time, geology, and astronomy. It is hard to fathom that 5,000 years ago when the Egyptians were building the Great Pyramids of Giza, they called alpha Draconis (Thuban), and not Polaris, the North Pole Star. Deep time, geology and astronomy can be philosophically harmonized through the concept of relativity.

    The physical science of relatively tells us that position, time and speed are related to how you seen the universe, and through the uncertainty principle, that position and time for an object cannot be known with certainty at the same instant. As we look out into the deep universe, we also look back in time, and we see distant galaxies in deep time, that is as they appeared and where they appeared millions and billions of years ago. Astronomers call this distance-then. But we cannot see where those galaxies are now or what they look like now, which astronomers call distance-now. As you shrink distance down to the level of our solar system and planet, and thus increase your certainty of position, we lose that ability to see deep time for terrestrial geology. Similarly, as you get closer to terrestrial distances, you lose the precision in your ability to perceive astronomical slow or deep time like precession.

    But the ability to see deep time in real time still exists. Geologists can barely see deep time – they can measure the infinitesimal speed of soil erosion that over millions of years created the Grand Canyon, and similarly astronomers see deep time as the very small rate of precession - 0.0138 degrees per years. Hold you index finger outstretched; its about 1/100th of the width of your fingernail per year. As precession accumulates over twenty years, it outdates astronomers’ star charts, and throw their old charts away and republish new ones.

    Kurt, SLC, UT

  4. Kelly,

    Your statement, "In 110 years, the pole has moved about 1.5 degrees closer to Polaris—the diameter of 3 full moons . . . Try to picture it: in about 200 years, the North Pole changes by about the diameter of 4 full moons,” could be improved by accounting for the differences between angular size at the poles and at the equator and that the speed of Polaris’s passage of the north celestial pole is not uniform over time. A practiced astronomical eye would discount your otherwise strong writing due to your writing not accounting for these differences. A more accurate summary would be currently, Polaris is a little more than 1 full Moon diameter from the pole (42 arcminutes / 30.1 arcminutes), and that in 500 years, Polaris will be about 6 full Moon diameters from the pole (per computations below).

    A more astronomically accurate statement would be as follows, but I have made no attempt to adjust or compress the language for a prose style, and I have included computations in parentheticals for the purpose of background: Over the next 200 years, precession will change the position of celestial objects near the equator by about 2.7 degrees (50.8 arcseconds * 200 yrs), or about 5 diameters of the full Moon (2.7 degs / (30.1 arcminutes/60 arcminutes per degree). The lines of celestial longitude converge at the celestial poles and this reduces the scale annual precession near the poles (by cos(declination). Polaris is at 89.25 degrees declination). Presently (2015), the distance between Polaris and the North Celestial Pole is about 40.25 arcminutes (0.67 degrees), and, in 200 years (22150) Polaris will still be about 40.62 arcminutes from the NCP. The change is only 0.04 arcminutes, or, adjusting for the 89.25 celestial latitude of the Moon, about 3 arcminutes, or one-tenth the size of the Moon (0.04 (cos(89.25 degs) = 3.0 arcminutes). The Moon’s diameter is about 30.1 arcminutes, or about one-half a degree.) Over the next 500 years, our descendants will see Polaris accelerate away from the Pole, and in 2715, Polaris will be 3.2 degrees from the celestial pole (planetarium program simulation), or about 6 full Moon diameters away from the pole. In deep time, that is 5,000 years (7015), about the same amount of time in the future as we relate to the building of the pyramids in 3015 B.C.E., Polaris will be about 19.3 degrees from the pole.

    I have not used Stellarium in some time, but it has some features that you can use to replicate these effects. Zoom in on Polaris and the North Celestial Pole (about a 10 degree field of view). There is a feature that allows you to zoom forward in time. See the Official User’s Guide, 3.1.1 Time Travel. ( ). There is an Angular Measure plug-in that you can activate to measure the distance between two objects. ( , ). Look at the North Celestial Pole, and then use the Time Travel features to advance forward to the desired point in the future. Then use the Angular Measure plugin to measure the distance between the pole and Polaris.

    That the size of a square degree differs at the equator and at the poles is an effect of foreshortening. The lines of longitude converge at the poles. Think of a map of the Earth’s surface. Angular distances at the poles are shorter than at the equator. That is why Greenland appears much smaller than it really is on a basic Mercator project map of the Earth.

    Again, I really enjoyed your writing, and the above is not intended as a criticism. I am suggesting an improvement of the quality of the facts in order to increase your good piece’s strength.

    Best, Kurt, SLC, UT

  5. Thanks Kurt for these illuminating comments, and I apologize for not getting to them sooner, as I've been away from internet-ing for a few days. I greatly appreciate the insight of one more mathematically experienced than I am. Thanks for taking the time to correct and clarify things!

  6. Cool post. Nice work with the polar photos!