Physicists measured the smallest gravitational force yet

Gravity is the weakest of all known forces in nature. The strength of gravity is determined by the mass of the Earth and the distance from the center. On the Moon, which is about 80 times lighter and almost four times smaller than the Earth, all objects fall six times slower.

On a planet the size of a ladybug, the objects would fall 30 billion times slower than on Earth. Gravitational forces of this magnitude normally occur only in the most distant regions of galaxies to trap remote stars.

The gold ball used in size comparison with a 1 cent coin. According to Einstein's general theory of relativity, every mass bends space-time (© Tobias Westphal / Arkitek Scientific)

In a recent study, quantum physicists led by Markus Aspelmeyer and Tobias Westphal of the University of Vienna and the Austrian Academy of Sciences have now demonstrated these forces in the laboratory for the first time. What’s more, they successfully measured the gravitational field of a gold sphere, just 2 mm in diameter, using a highly sensitive pendulum — and thus the smallest gravitational force.

For the study, scientists drew on a famous experiment conducted by Henry Cavendish at the end of the 18th century. In his work, Cavendish used a smart pendulum device to measure the gravitational force generated by a lead ball 30 cm tall and weighing 160 kg in 1797. A so-called torsion pendulum — two masses at the ends of a rod suspended from a thin wire and free to rotate — is measurably deflected by the gravitational force of the lead mass. Over the coming centuries, these experiments were further perfected to measure gravitational forces with increasing accuracy.

In this new study, scientists picked up the idea of Cavendish. They also developed a miniature version of the Cavendish experiment. A 2 mm gold sphere weighing 90 mg serves as the gravitational mass. The torsion pendulum consists of a glass rod 4 cm long and half a millimeter thick, suspended from a glass fiber a few thousandths of a millimeter in diameter. Gold spheres of similar size are attached to each end of the rod.

The tiny pendulum is suspended from a thin glass fiber and feels the gravitational force of the millimeter-large gold ball (© Tobias Westphal)

Jeremias Pfaff, one of the researchers involved in the experiment, said, “We move the gold sphere back and forth, creating a gravitational field that changes over time. This causes the torsion pendulum to oscillate at that particular excitation frequency.”

Using laser, scientists were able to read the movement, which is only a few millionths of a millimeter. It also helps them conclude the force. The difficulty is keeping other influences on the motion as small as possible.

Co-author Hans Hepach said, “The largest non-gravitational effect in our experiment comes from seismic vibrations generated by pedestrians and tram traffic around our lab in Vienna. We, therefore, obtained the best measurement data at night and during the Christmas holidays, when there was little traffic.”

“Other effects such as electrostatic forces could be reduced to levels well below the gravitational force by a conductive shield between the gold masses.”

Scientists also determined Other effects such as electrostatic forces could be reduced to levels well below the gravitational force by a conductive shield between the gold masses. In the future, scientists planned to investigate the gravity of groups thousands of times lighter.

First author Tobias Westphal said, “According to Einstein, the gravitational force is a consequence of the fact that masses bend spacetime in which other masses move. So what we measure here is how a ladybug warps spacetime.”

Journal Reference:

Tobias Westphal, Hans Hepach, Jeremias Pfaff, Markus Aspelmeyer. Measurement of gravitational coupling between millimeter-sized masses. Nature, 2021; 591 (7849): 225 DOI: 10.1038/s41586-021-03250-7

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