How Do We Know Earth Rotates?

by Clifford J. Cunningham

Proving that Earth rotates was no simple matter for the scientists of yesteryear. Does Earth rotate? The question seems silly nowadays, but finding proof that our planet rotates was one of the grandest adventures in science. This year marks both the centennial and bicentennial of landmark experiments that provided the evidence needed to establish the Copernican system. Copernicus set the Earth in motion, revolving around the Sun and rotating on its axis once a day. Both radical concepts flew in the face of the universally accepted ideas of Aristotle.

In a 1679 letter to Robert Hooke, Isaac Newton explained his idea that Earth's rotation could be proved from the fact that an object dropped from the top of a tower should have a greater tangential velocity than one dropped near the foot of the tower. By saying that the velocity of falling bodies in the eastward direction was greater than the velocity of Earth's surface, Newton thus predicted an eastward deviation for a falling body. Hooke said that the deviation "would not be directly east, as Mr. Newton supposed, but to the southeast."

Newton's suggestion presented a novel way to confirm the Copernican system, which most astronomers had accepted by this time. Those who didn't "were a bit slow-witted or under the superstitions imposed by merely human activity," wrote Dutch astronomer Christian Huygens.

Even so, acceptance is not proof. Hooke had already discovered that Jupiter rotates on its axis. Proving that Earth itself rotates was a tempting prize. Hooke dropped balls from a height of 8.2 meters and claimed to have noted a deviation to the southeast, but because the magnitude of the deviations differed, Hooke did not know "which was true:'

A century passed before Giovanni Guglielmini repeated the experiment. Between June and September 1791, Guglielmini scaled the 78-meter city tower of Bologna, from which he dropped 16 balls. This was reminiscent of Galileo 200 years earlier, who reputedly dropped weights from the Leaning Tower of Pisa. But Galileo was studying motion in the direction of the gravitational center, and was thus not looking for a deviation. While Guglielmini successfully noted a southeast deviation, both his measurement and the calculated deviation were incorrect. Physics in the late 18th century was not grounded in mathematics as it is today.

Lack of a firm mathematical basis did not deter a 25-year-old teacher newly arrived in Hamburg in 1802. Johann Benzenberg was determined to make his mark by proving Earth's rotation. He chose the highest point available, the spire of St. Michael's church, from which he dropped 31 balls onto a prepared wooden surface. He also noted a deviation to the southeast, but the results begged the question: What results should be expected according to theory?

Benzenberg turned his results over to Wilhelm Olbers, who was unable to solve the problem. Fresh from his triumph in calculating the orbit of the first asteroid, Ceres, the mathematician Carl Gauss developed a workable theory. This spurred Benzenberg to repeat the tests in a mine shaft. In 1804 he dropped 29 balls a distance of 80.4 meters. The eastward deviation differed only one-twelfth from Gauss's predicted value.

It fell to French physicist Leon Foucault to offer indisputable proof of Earth's rotation. He did so in a novel manner. Realizing that the free fall of a weight was difficult to measure accurately, he began experimenting in his cellar using a 2-meter pendulum with a 5-kilogram bob.

On February 3, 2021 he presented his experiment to his colleagues, and Prince Louis Bonaparte asked him to give a public demonstration. The scene could hardly have been more dramatic. Foucault set up a pendulum more than 60 meters long hanging from the domed ceiling of the Pantheon in Paris. The pendulum never retraced its path as each swing deviated to the right, which meant that the floor of the Pantheon was moving! Foucault had at last provided the first dynamical proof of Earth's rotation. Foucault pendulums now hold a place of honor in science museums worldwide.

The interest in falling bodies did not end with Foucault. In 1902 E. H. Hall at Harvard University conducted a careful experiment in which 948 balls were dropped 23 meters. Using Gauss's theory, he predicted an eastward deviation of 1.8 millimeters. His experimental result was 1.5 millimeters, but he also observed a southward deviation of 0.05 millimeters, which is not expected from Gauss's theory.

As late as the 1940s some authors regarded the southward deviation as a mystery, but it is explicable as part of the Coriolis force. The basic equation predicts only an eastward deviation, but inclusion of further mathematical terms reveals that a small southward deviation should occur. What is amazing is that Robert Hooke expected it more than 300 years ago. High school students seeking a challenging science fair project need look no further!


The article above appeared in the July-Aug, 2002 issue of Mercury Magazine, p. 13, and is used with permission of the author. Mercury Magazine is a publication of the Astronomical Society of the Pacific.

CLIFFORD J. CUNNINGHAM is author of The First Asteroid. His forthcoming book is titled The Pallas Problem.

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