Stick-in-the-Mud Astronomy

By Neil deGrasse Tyson

Natural History Magazine

You'll need your brain and plenty of patience—but not much more—to take the measure of the Earth and its motions.

In modern times, various blends of high technology and clever thinking drive cosmic discovery. But suppose you had no technology. Suppose all you had in your laboratory was a stick. What’s there to learn? With patience and careful measurement, you and your stick can glean a ridiculous amount of information about our place in the cosmos. The stick’s material doesn’t matter. Neither does its length. Nor its color. It just has to be straight.

First, hammer the stick vertically and rigidly into the ground at a location in clear view of the horizon. Might as well us a rock for a hammer, since you have no technology. A stick in the ground is also called a gnomon, but I prefer the word stick. On a clear day, track the length of the stick’s shadow as the Sun rises, crosses the sky, and then sets. The shadow will start long, get shorter and shorter until the Sun reaches its highest point in the sky, then lengthen again until sunset. This activity is about as exciting as tracking the hour hand on your watch. But without technology, not much else is going on to compete for your attention. You will notice from this exercise that the middle of the day occurs when the shadow is at its shortest. At that moment, the shadow points due south, if you are north of Earth’s equator, and due north if you are south of the equator. That moment is what we now call local noon, and repeats daily—something we take for granted.

If you have the patience to repeat this exercise three hundred and sixty five times in a row, you will notice from day to day that the Sun doesn’t rise at the same spot on the horizon. Twice a year, the shadow of the stick at sunrise will point exactly opposite the shadow of the stick at sunset. When this happens, the Sun rises due east, sets due west, and the length of daytime hours equals the length of night. These are the spring and fall equinoxes, Latin for “equal night.” For all other days of the year, the Sun rises (and sets) someplace else on the horizon. So the adage “the Sun always rises in the east and sets in the west” was invented by somebody who never paid attention. The sunrise spot will creep north of the east-west line. Eventually slow down. Stop. And then creep south for a while. After crossing the east-west line it will slow down. Stop. And then repeat. All the while, the Sun’s trajectory changes; when the Sun rises farthest north of east, it traces its highest path across the sky, making the shortest noon stick shadow of the year. That day is the summer solstice, Latin for “stationary Sun.” When the sun rises far south of east, its trajectory across the sky is low, making for a long stick shadow at noon. That day is the winter solstice. For most of Earth’s surface, the Sun at noon is never directly overhead. For other parts of Earth, the sun is directly overhead at noon on only two days of the year. So the adage, “at high noon the Sun is directly overhead” must have been started by the same ignorant person who professed to know where on the horizon the Sun rises and sets.

With a stick and some patience we have identified the cardinal points on the compass and the four days of the year that mark the change of seasons. If you now find some way to time the interval between one day’s noon and the next, you can determine, to high accuracy, the rate that the Sun appears to revolve around Earth—the solar day. Averaged over the entire year, this time interval equals 24 hours, exactly, not including the occasional leap second we add now and then to account for the slowing of Earth’s rotation by the action of the Moon’s tidal forces of gravity.

If you park yourself near the stick, establish a line of sight from its tip to a spot on the sky, and then mark your timer when a star passes by, you can measure the time between successive alignments with the same star. Using a familiar clock this interval is 23 hours, 56 minutes, 4.1 seconds—the sidereal day. The four-minute daily mismatch between the sidereal; day and the solar day forces the Sun to move against the background stars throughout the year, giving the illusion that the nearby Sun visits the stars from constellation to another. This led ancient peoples to presume that the legends and mythologies of the sky actually influenced the personality of those born when the Sun was in a particular “sign.” Remarkably, such belief systems persist in several cultures today, one of which is located in Earth’s northern hemisphere, on a land-mass between the Pacific and Atlantic oceans.

Equipped now with a watch to measure accurate time, you can now try something different with your stick in the ground. Instead of timing how long it takes between times when the stick’s shadow is shortest, for an entire year, place a mark on the ground where the tip of the stick’s shadow falls at twelve noon, as measured on your watch. From day to day, you will not return to the same spot on the ground. Your etchings will trace a figure-eight, revealing an orbital subtlety: Earth’s orbit around the Sun is not a perfect circle. As a consequence, our orbital speed varies, growing as we near the Sun, diminishing as we recede. Since Earth’s rotation rate stays rock-steady during all this, something has to give: the Sun does not always reach its highest point on the sky at clock-noon. While the shift is slow from day to day, the Sun gets there up to fifteen minutes later during parts of the year. At other times of the year, fifteen minutes early. The only four days when clock time equals Sun time, corresponding to the top, bottom and middle of the figure-eight, are April 15 (no relation to the IRS), June 14 (no relation to flags), September 2 (no relation to Labor Day), and December 25 (no relation to Jesus).

This figure-eight has the name analemma, and is carved on every sundial, along with instructions on when to add or subtract minutes to the time read by shadow, to convert to real time. The anlemma, also known as the equation of time, is often drawn afloat in the expanse of the Pacific Ocean by globe makers, who clearly had nothing else to put there.

Next up, clone yourself and your stick and send your twin due south some prearranged distance, but far beyond your horizon. Agree in advance that you will both measure the length of your stick shadows at the same time on the same day. If the shadow lengths are the same, you live on a flat, or a very, very large Earth. If the shadow lengths are different, you can use simple geometry to calculate Earth’s circumference. The Greek mathematician Eratosthenes (276–194 BC) did just this. Comparing shadow lengths in the two Egyptian cities, Alexandria and Syrene (separated from each other by 4,300 stadia) Eratosthenes derived Earth’s circumference within ten percent of the correct value. Indeed, the word geometry, itself, hails from the Greek, meaning “earth measurement.”

All that activity took a few years. The next stick experiment will take about minute. Hammer your stick into the ground at an angle other than vertical—resembling a stick in the mud. Dangle from the stick’s tip a bob at the end of a thin string. Measure the length of the string and then tap the bob to set the pendulum into motion. Count how many times the bob swings in a minute. The number, it turns out, depends very little on how wide the pendulum swings. And it depends not at all on the mass of the bob. Only on the length of the string and what planet you are on. Using a relatively simple equation of physics, you can educe the acceleration of gravity on Earth’s surface. On the Moon, with one-sixth the gravity of Earth, the same pendulum will move much more slowly, giving many fewer swings per minute. There’s no better way to take the pulse of a planet.

Up till now, the stick offered no proof that Earth, itself, rotates. Only that the Sun and nighttime stars move at regular, predictable intervals. If you now use a very long tilted stick. Perhaps ten meters in length. And once again hammer it into the ground at an angle. And once again dangle a heavy bob from the end of a long thin string on its tip. And once again, set it into motion. The thin, long string and the heavy bob will resist friction at the pivot, enabling the pendulum to swing for hours and hours, unencumbered by its attachments.

If you track the plane in which the pendulum swings, and if you are patient, you will notice that the plane slowly rotates, being a direct measure of Earth’s rotation. The most pedagogically useful place to do this experiment is on the North Pole, where the plane of the pendulum’s swing makes one full revolution in twenty-four hours, betraying the rotating Earth beneath it. For all other locations on Earth, except the Equator, the plane still rotates, but takes longer and longer per revolution as you move from the poles to the equator. On the equator, the pendulum’s plane does not move at all. This experiment not only demonstrates that Earth is what moves and not the Sun, but, with a little bit of trigonometry, you can reverse the question and use the time for one cycle of the pendulum’s plane to determine your latitude on Earth.

This classic demonstration was first performed in 1851 by Jean Leon Foucault, a French physicist who surely conducted the last of the truly cheap laboratory experiments. There’s a Foucault pendulum in practically every science and technology museum in the world. Instead of dangling from a stick, they usually dangle from the highest ceiling among the Museum building.

Given all we have learned with just a stick in the ground, what are we to make of famous prehistoric observatories? A survey of the world’s ancient cultures turns up, in almost every case, stone monuments that served as low-tech astronomical centers. Civilizations in South America, Europe, Asia, and Africa are on this list. It’s likely that these observatories also doubled as places of worship or contained meaning that was otherwise deeply cultural. At Stonehenge, for example, in the Salisbury Plain of England, the circle of huge monoliths (up to 60 tons each) are made of a stone not available in the immediate area. Some stones were taken from a site 24 miles away in Marlborough Downs while others were transported by raft from a site in the Prescelly Mountains in southwestern Wales, 140 miles away.

Much is written about the astronomical significance of the site. Historians and casual observers alike remain impressed with the astronomical knowledge of these ancient peoples. In particular, the stones align with the sunrise point on the summer solstice, attracting throngs of tourists annually, some moved to tears. Some fantasy-prone observers even credit alien intervention at the time of construction. Quite a compliment, I would say.

Why the ancient Celtic civilizations who built the thing did not use easy, nearby rocks remains a mystery. But the fact that Stonehenge exists is not. Construction lasted more than a millennium. You can build anything in a thousand years—I don’t care how far you have to drag your bricks. Furthermore, the science of Stonehenge is not fundamentally deeper than what we discovered with our stick in the ground.

Perhaps these ancient observatories perennially impress modern people because modern people have no idea how the Sun, Moon, or stars move. We are too busy watching evening television to care what’s going on in the sky. So to us, a simple rock alignment with the cosmos looks like an Einsteinian feat. The truly mysterious civilizations may, instead, be the ones that made no cultural or architectural reference to the sky at all.