The Triumph of Newton’s Law of Gravity in Its Greatest Test in History

According to SAEDNEWS, citing Faradeed, scientists used data from the Atacama Cosmology Telescope to test Newton’s law of gravity at the scale of galaxy clusters and distances of hundreds of millions of light-years. The results showed that gravity at these extremely large scales still approximately follows Newton’s inverse-square law.

Researchers used the positions and velocities of hundreds of thousands of galaxy clusters as well as the effects of the cosmic microwave background radiation. The data showed that the dependence of gravity on distance is consistent with a power of about 2.1, which is very close to Newton’s prediction.

At the same time, the results place serious challenges on alternative theories such as Modified Newtonian Dynamics.

More than three centuries after Newton proposed the law of universal gravitation, cosmologists have now been able to test it on the largest known scales in the universe and confirm it. This law, known as the “inverse-square law,” states that the gravitational force between two masses is inversely proportional to the square of the distance between them; meaning that as distance increases, the force rapidly decreases.

The inverse-square law had previously been confirmed in terrestrial experiments and also at the scale of the solar system, but a new study has extended it to unprecedented scales: galaxy clusters separated by hundreds of millions of light-years.

According to Priyamvada Natarajan, an astrophysicist at Yale University, Newton’s law of gravity had previously been tested with high precision on Earth and within galaxies, but now it has been examined on cosmic scales for the first time. She says this result is not unexpected, but it could challenge alternative theories such as Modified Newtonian Dynamics (MOND), which attempts to explain galactic behavior without dark matter.

Newton’s law, published in 1687 in his famous work Mathematical Principles of Natural Philosophy, was able to explain planetary motion using Johannes Kepler’s empirical laws. About a century later, Henry Cavendish confirmed the law in a laboratory using a torsion balance experiment, in which the gravitational force between small objects was measured by detecting the twist of a very thin wire. Today, even more precise versions of the same experiment are used to test possible new forces at very short distances.

In the new study, a group of scientists using the Atacama Cosmology Telescope in Chile tested Newton’s law on the largest structures in the universe, namely galaxy clusters. Each galaxy cluster can contain hundreds of galaxies bound together by mutual gravity. The mass of a cluster can reach up to about one quadrillion times the mass of the Sun, with sizes of tens of millions of light-years.

According to Science, researchers combined data from hundreds of thousands of galaxy clusters using two independent types of measurements: their spatial positions and their velocities. Just as planets closer to the Sun move faster, galaxy clusters that are closer to each other also tend to move faster relative to one another. Therefore, the relationship between distance and relative velocity can provide direct information about the nature of gravity.

However, this relationship is not simple to calculate, since each cluster’s motion is influenced not only by its own gravity but also by all surrounding clusters. To solve this, researchers first used data from the Sloan Digital Sky Survey (SDSS), which has mapped millions of galaxies since 2000, to determine the spatial distribution of galaxies. They then applied a general force law with adjustable parameters to this distribution to predict how the relative velocities of cluster pairs change at different distances.

To avoid the effects of cosmic expansion and dark energy, researchers only examined clusters located between 5.6 and 7.7 billion light-years from Earth. They measured extremely small accelerations of about 10 femtometers per second squared, roughly a quadrillion times weaker than Earth’s gravitational acceleration.

The final result showed that gravity on scales of 80 to 800 million light-years still follows Newton’s inverse-square law, with its dependence on distance being close to a power of about 2.1. This result is effectively a very precise confirmation of classical gravity on the largest observable scales.

The findings pose challenges for Modified Newtonian Dynamics. This theory, proposed in the 1980s, attempts to explain the unusual rotation of galaxies without assuming dark matter, by modifying Newton’s second law (force equals mass times acceleration) at very small accelerations. However, if MOND were correct, one would expect that on very large scales the dependence of gravity on distance would be nearly linear rather than quadratic. The new results do not show such behavior, thereby further challenging this theory.

Finally, the researchers emphasize that their study is not only an important test of gravity but also demonstrates the power of measuring galaxy cluster velocities using the Sunyaev–Zel’dovich effect. According to cosmologists, next-generation instruments such as the upcoming Simons Observatory will measure with much higher precision and may help further investigate dark matter, dark energy, and the history of the universe’s expansion.