How Does Foucault’s Pendulum Prove the Earth Rotates?
This elegant scientific demonstration has been delighting everyday people for nearly 200 years
On February 3, 1851, a 32-year-old Frenchman—who’d dropped out of medical school and dabbled in photography—definitively demonstrated that the Earth indeed rotated, surprising the Parisian scientific establishment.
Acting on a hunch, Léon Foucault had determined that he could use a pendulum to illustrate the effect of the Earth’s movement. He called together a group of scientists, enticing them with a note declaring, “You are invited to see the Earth turn.” Foucault hung a pendulum from the ceiling of the Meridian Room of the Paris Observatory. As it swept through the air, it traced a pattern that effectively proved the world was spinning about an axis.
A month later, Foucault shared his experiment with all of Paris at the majestic Pantheon building. According to the American Physical Society, he suspended from the Pantheon’s lofty dome a 61-pound brass bob on a 220-foot cable. As it swung back and forth, the pointed end of the bob traced lines in sand that had been poured on a wooden platform. Over time, the angle of these lines changed, suggesting to audience members that the direction of the pendulum’s travel was shifting under the influence of an unperceived rotational motion—that of Earth.
Foucault was able to demonstrate a scientific concept in a way that the average person could easily grasp, says Rebecca C. Thompson, head of public outreach for the APS. For centuries, it was a commonly held belief that the Earth rotated on an axis. But it was Foucault who dispelled lingering doubts once and for all, establishing the phenomenon firmly in the realm of fact. “It really started the cultural shift to fundamentally understanding our universe differently,” Thompson says.
The experiment was a hit, drawing flocks of fascinated Parisians and catapulting Foucault to fame. Pendulums based on Foucault’s calculations began appearing worldwide—and are still iconic features of many science museums in the U.S. and other countries.
The Smithsonian Institution made a pendulum a focal point of its Museum of History and Technology (which later became the National Museum of American History). The building—which opened in 1964 on the National Mall in Washington, D.C.—was designed purposely to accommodate a pendulum. It hung from the ceiling of the third floor and stretched 71 feet through the center of the building, where it swung slowly and rhythmically across a fancifully emblazoned circle on the first floor. The Smithsonian pendulum was intended to be viewed from above, on the second floor.
Looking down, visitors would see a symmetrical hollow brass bob weighing about 240 pounds and shaped like an inverted teardrop. As it moved back and forth—facilitated by an electromagnetic push to keep it continuously swinging despite air resistance and vibrations in the cable—it would knock down inch-or-so-high pins standing at fixed points along the circumference of a small circle. Over time, viewers could see the direction of the pendulum’s swing change, implying that the Earth was rotating beneath them.
The Smithsonian pendulum, like all pendulums, moved in accordance with Foucault’s sine law, which predicts how much a pendulum’s path will distort each day based on its latitude. Absent any exterior forces, a pendulum would swing back and forth in a single plane forever—there would be no gradual angular shift. But the Earth is rotating, so the story isn’t that simple.
Since all points on Earth’s surface rotate as a unit, it follows that those located on the wider portions of the planet—nearer to the equator—must cover more meters each second (i.e., go faster) to “keep up” with the points tracing smaller circles each day at the extreme northern and southern latitudes. Though they don’t feel it, a person standing in Quito, Ecuador, is moving with appreciably higher velocity than one in Reykjavik, Iceland.
Because each swing of a pendulum takes it from a point farther from the equator to a point nearer to the equator and vice versa, and the velocities at these points differ, the path of the pendulum is subtly distorted with every swing, gradually torqued away from its original orientation. The extent of this effect depends on where on Earth the pendulum is swinging.
At the North Pole—where small changes in latitude have big implications—the path traced by a pendulum would shift through a full 360 degrees in a mere 24 hours, explains Thompson. At the equator, meanwhile, a pendulum’s motion would not be seen to distort at all.
Using his sine law, Foucault predicted that the path of his pendulum in Paris would shift 11.25 degrees each hour, or 270 degrees in a day. And it did.
His sine law allows anyone with a decent grounding in trigonometry to use a pendulum to determine their latitude. But mostly, at museums around the world, the pendulum has become an object that elicits wonder.
As iconic as the elephant that greets visitors in the rotunda of the Smithsonian’s National Museum of Natural History, the pendulum at the History and Technology museum was a meeting place, a striking backdrop for reflection and education. “It was very much like a fountain in a park,” says Peter Liebhold, a curator in the division of work and industry at the American History Museum.
Children and adults alike would stare at the pendulum, meditating on its motion and meaning. One morning in 1998, before the museum had opened, the cable snapped, sending the massive bob hurtling towards the floor, narrowly missing a staffer.
Rather than repair the cable, the museum elected to retire Foucault’s pendulum. Its director at the time decided the device did not have much to do with either America or history, says Liebhold.
The decision divided staffers. “There were pendulum huggers and pendulum haters,” Liebhold says. Pro-pendulum employees said it was cool and fun to watch. The anti-pendulum group believed it didn’t add much to the museum’s efforts to teach the public about American history and culture.
Though Liebhold says he was in the haters’ camp, he believes pendulums have their place, just elsewhere. A pendulum “makes the masses more trusting of the power of science,” he says.
Thompson agrees, and notes that while the pendulum is no longer needed to prove that the Earth rotates, “it is useful if we can get kids engaged in science.”