ANN ARBOR—Sky watchers contemplating the moon this month may wonder how far away it is. According to University of Michigan astronomer Richard Teske, the moon is 15 billion inches from Earth—give or take an inch.

Mix together the moon, four reflecting mirror arrays on its surface and five Earth-based telescopes firing laser beams and you have a recipe for one of the most accurate scientific experiments ever undertaken. “Determining the moon’s distance to within one inch is an extraordinary accomplishment,” Teske said. “These exquisite measurements—a kind of scientific slam-dunk—are being used to test Albert Einstein’s theory of gravity.”

The moon measurement project is an international effort. Mirrors were placed on the moon’s Earth-facing hemisphere by three teams of Apollo astronauts and by one of the unmanned Soviet Lunakhod missions. Telescopes used for beaming laser light at the moon are located in Texas, Hawaii, France, Germany and Australia.

In the experiment, laser radiation launched toward the moon from one of the telescopes on Earth bounces off one of the lunar mirrors and returns to the same telescope about 2.6 seconds later. Scientists determine the moon’s distance by measuring as precisely as possible the time it takes laser pulses to make the round trip. Called laser ranging, the technique is equivalent to using radar, Teske explained.

At stake is the dependability of Einstein’s theory of gravity as expressed through his complicated equations of relativity. The theory is used to predict the moon’s distance from Earth from moment to moment as it orbits our planet once each month. The laser ranging experiment checks out those predictions with actual, accurate observations.

“Right now all is well with Einstein. Relativity’s predictions seem to be correct, reinforcing physicists’ beliefs that the theory is the best description we have for how nature operates,” Teske said. “But there are other theories of gravity that also are being examined by the experiment, and it is still too early to rule them out altogether. Since the laser ranging experiment will go on for a few more years, we might eventually find that one of those theories is preferable to Einstein’s. If so, science will have taken a great stride in our understanding of how the universe works.”

Keeping track of the moon as it orbits around Earth is tricky, Teske added. In addition to our planet’s gravitational pull, the moon is strongly tugged by the sun and weakly attracted by all the planets and even some small asteroids. As a result, it meanders a lot during its month-long orbit. A further complication is that the moon doesn’t simply circle around Earth’s center.

“Both Earth and the moon circle one another around a common point that is located 1,025 miles beneath Earth’s surface,” Teske said. “As our planet rotates on its axis that point travels through solid rock with the speed of a jet airplane, but with no discernible effect upon us or the Earth.”

Gravity experimenters also take into account the fact that the moon’s orbit is affected by random variations in the rate of the Earth’s rotation, which are caused mainly by the interaction of the Earth’s surface with its atmosphere. To compensate for these variations, scientists must occasionally insert an extra second into the stream of time.

“Both cycles will finally fall into step in the dim, far future when the Earth will keep the same face toward the moon just as the moon now keeps the same face toward us,” Teske said. “Perhaps by then nobody will much care whether Albert Einstein was right.”

University of Michigan