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Features May 2007: Volume 4, Number 2

Shooting the Moon
By Kim A. McDonald

A modern-day version of Galileo’s experiment seeks to test Einstein’s general theory of relativity.


Tom Murphy got jazzed about astronomy in high school when Halley’s Comet streaked by in 1986. He read about the five spacecraft from the USSR, Japan, and the European Community that visited the comet, and th en went on to study the history of the Apollo lunar missions. But he never imagined he’d be shooting lasers at the moon.

An assistant professor of physics at UCSD’s Center for Astrophysics and Space Sciences, Murphy’s love “for all things astronomy” led him to Caltech, where he obtained his doctorate and built a novel infrared spectrograph for the Palomar Observatory. Then, he “switched gears” as a postdoctoral fellow at the University of Washington, where he got interested in problems of fundamental physics. Now he’s back in Southern California, spending nights on the fourth floor of the Science and Engineering Research Facility directing a New Mexico telescope via computer to shoot pulses of laser light at the moon.

The reason? To determine if Galileo or Einstein may have been wrong.

More than 400 years ago, as the apocryphal story goes, Galileo dropped cannon balls, musket balls, wood and other objects from the Leaning Tower of Pisa and discovered that lighter objects hit the ground at the same time as the denser, more massive ones. Galileo concluded that gravity accelerates all objects equally, regardless of their mass or composition. It’s a cornerstone of modern physics that physicists call the “equivalence principle.”

Einstein constructed his theory of gravity—the general theory of relativity—based on that principle. And physicists since then have shown Einstein’s theory and the equivalence principle to be largely correct.

But what if the objects of different mass and composition Galileo dropped were as big as the Earth and moon? And what if they fell not from the 183-foot-high Tower of Pisa, but from the 93 million mile distance between the Earth and the sun? Do the Earth and moon fall toward the sun at exactly the same rate? Or is the moon’s orbit slightly skewed, either toward or away from the sun, suggesting that something is wrong with Einstein’s theory?

That, in a nutshell, is what Murphy wants to find out. His modern day version of Galileo’s experiment, financed by NASA and the National Science Foundation, is no easy task. To find any deviations from the predicted orbit of the moon, he must measure the distance from the Earth to the moon to within the accuracy of a millimeter, or about the thickness of a paperclip.

Decades of lunar-ranging experiments by NASA’s Jet Propulsion Laboratory in Pasadena have allowed physicists to measure the distance from Earth to moon to within 1.7 centimeters. (It is 238,700 miles on average, varying by plus or minus six percent as the moon goes around the Earth). Murphy’s goal is to do 10 times better.

To accomplish that task, he and UCSD graduate student Eric Michelsen have, for the past year, been sending pulses of laser light from the Apache Point Observatory, near White Sands, New Mexico, to suitcase-sized reflectors left on the moon by the Apollo astronauts. Their project, appropriately dubbed APOLLO for Apache Point Observatory Lunar-Laser-ranging Operation, is fairly straightforward: Collect photons of light that return from those reflectors and measure the time it takes light to travel to the moon and back. Since they know the speed of light, the one-way travel time gives them the precise distance from Earth to moon.

The difficulty with this technique, called lunar-ranging, is getting enough photons. Since the pulse of laser light spreads outward like a flashlight beam, only a tiny fraction of the photons ever hits the reflectors on the moon. An even smaller fraction returns to the telescope. The process is statistically akin to tossing a 100-meter cube of beach at the moon, then waiting for a single grain of sand to return.

“Only one out of 30 million photons hit the reflector,” says Murphy. “And of those lucky ones that do, only one out of 30 million return to the telescope.”

To measure the distance from Earth to moon with one millimeter precision, the physicists confront another seemingly impossible challenge: They must measure the time for the photons to make the roundtrip to within a trillionth of a second.

“We send 20 pulses per second and it takes two and a half seconds for each pulse to make its round trip, so the net effect is that we have 50 pulses that are out at any given time,” Murphy says. “Since we have 50 balls in the air at any one time, we can’t drop any of them or we’d get confused over which one is which.”

Add to this mix the cloudy nights, rain and high winds that prevent the physicists from using their telescope on this remote, wind-swept, bitterly cold mountain peak in New Mexico’s Sacramento Mountains on about half of their 10 scheduled observing nights a month, and Murphy admits the experiment has become much more difficult than first envisioned. “This whole business can be very frustrating,” he says. “We had a few runs in the last lunar month where we didn’t see any signals at all.”

“ I wanted to get into this project because it was fun, I could build this apparatus, shoot lasers at the moon, measure something about general relativity,” Murphy explains. “But when I started this project in September 2000 as a postdoc at the University of Washington, I didn’t have any idea it would take this long. I thought that by the time I left I’d be shooting lasers at the moon, but it was actually 5 years later that we were finally doing this and getting returns. And it was another year before we got into this steady campaign. I’ve never worked on one thing for so long.”

Some people ask him why he would devote himself to a single experiment that takes so much time, so much detail and probably has very little chance of overturning Einstein or Galileo. Murphy nods in partial agreement.

“We’re dealing with things in basic physics that are very hard to do, because all of the easy things have been done. The safe bet is that we won’t find anything wrong with general relativity. And the reason for that is that already at a part in one thousand, the lunar orbit shows that Einstein’s theory is correct. If we push it another order of magnitude, to a part in ten thousand, it’s an incremental improvement. But you never know until you check. I’d rather do the experiment and know that general relativity is good to another order of magnitude than just assume it is. That’s not the way science is done.”

Aside from testing the equivalence principle, Murphy points out that APOLLO has other practical benefits. The precise lunar orbit that he and his team develop should provide planetary scientists with more information about the moon itself. “It will help us understand more about the lunar interior,” he says. “How does the moon react to torques? Does the moon have a solid or liquid core? All of this may tell us something generally about the formation of solid bodies.”

The past year of regular measurements by APOLLO, in fact, has already improved the existing information about the moon’s orbit. “It’s confirmed that we are roughly at the half centimeter error level. After a year’s worth of one to three millimeter data, we should have a better understanding of the lunar orbit and gravitational physics.”

By 2008, Murphy says APOLLO should allow his team to take a first stab at answering the question of whether Einstein and Galileo were right. And that’s given him the optimism and confidence to continue for the long haul.

“I feel lucky to be doing something that people can understand, and that relates to our legacy and space exploration. Also I feel that I’ve been able to personally experience the Apollo lunar landings, because now I’m finally seeing photons come back from those reflectors.”

Kim McDonald is director of science communications at UCSD.


UCSD’s Center for Astrophysics and Space Sciences

Tom Murphy, Assistant Professor in UCSD's Physics Department

APOLLO Project

"Decades of lunar-ranging experiments by NASA’s Jet Propulsion Laboratory in Pasadena have allowed physicists to measure the distance from Earth to moon to within 1.7 centimeters. "