Shooting the Moon

Laser light aimed at reflectors left on lunar surface could pinpoint distance from Earth – and test Einstein's theory

By Bruce Lieberman
San Diego Union-Tribune

July 13, 2006

On July 21, 1969, Neil Armstrong and Buzz Aldrin propped an array of reflectors in the lunar soil – one of several science experiments they deployed a day after becoming the first humans to set foot on the moon.

A month later, a small group of astronomers bounced a pulse of laser light off the reflectors and caught the return signal with a telescope at Lick Observatory near San Jose, in Northern California. By measuring the time it took for the pulse traveling at the speed of light to return, scientists could determine the distance between the Earth and moon.

And so in the summer of 1969, the era of modern lunar ranging was born. Today, 37 years later, scientists at UCSD are firing lasers at the same reflectors. Equipped with 21st-century technology and new techniques, they plan to measure the distance between the Earth and moon down to an astounding 1 millimeter – the width of a paper clip.

Why do this at all? There are several reasons.

Lunar ranging has revealed several insights into the interior and orbital mechanics of both the moon and Earth.

One is that the moon is spiraling away from Earth at a rate of about 1.5 inches a year, due to ocean tides on Earth. Another is that the moon probably has a liquid core.

Lunar ranging has helped scientists better understand the rise and fall of tectonic plates – which vary the Earth-moon measurements – and the forces beneath the ground that cause those seismic movements.

And then there's Einstein's theory of general relativity.

As an explanation for the nature of gravity, general relativity relies on a key assumption: that gravity accelerates all objects at the same rate – regardless of their mass or composition. This idea is called the equivalence principle.

Galileo Galilei, according to some accounts, tested the equivalence principle 400 years ago when he dropped cannon and musket balls, gold, silver and wood from the Tower of Pisa – and they all hit the ground at the same time.

As the Earth and moon orbit the sun, therefore, they should be “falling� toward it at the same rate of acceleration – just like the cannon and musket balls falling toward the ground.

That “equivalence� of acceleration around the sun should reveal itself as predictable orbital paths for the Earth and moon that scientists can calculate.

That's where lunar ranging comes in. By measuring the distance between the Earth and the moon, repeatedly throughout about a year, scientists can calculate the orbital paths of the Earth and moon around the sun – relative to each other.

A violation of the equivalence principle would show up in lunar ranging data as a skewing of the moon's orbit around the Earth, either toward or away from the sun.

Lunar ranging experiments conducted at various observatories around the world so far confirm the equivalence principle, so Einstein's theory appears safe. But more precise efforts could upend general relativity and usher in a revolution in physics.

“What it would mean to me is that I would probably spend the next several years trying to figure out why my experiment is lying to me,� said Tom Murphy, a UCSD physicist who is leading a new lunar ranging project at Apache Point Observatory in New Mexico. “I wouldn't immediately adopt or trust the result.�

Neither would other physicists, he said. “A single experiment that flies in the face of all that's been holy for the better part of a century is not likely itself to bring about a revolution.�

But it would raise some eyebrows and create a rush to replicate the findings.

“A second experiment showing the same consistent result might be enough to actually promote a revolution.�

Unifying theory

For decades, scientists have searched for one unifying theory that explains the nature and behavior of space, time, matter and energy in the universe. Currently two dominant theories explain much of what scientists observe either directly or indirectly: general relativity and the standard model of quantum mechanics.

Einstein's famous theory of general relativity, first published in 1916, explains gravity and motion by uniting three-dimensional space and time into four dimensions that together create an elastic fabric of reality called space-time that is warped by the energy it contains. In this theory, mass is one form of energy, and it creates gravity by warping space-time.

In quantum mechanics, space and time form a flat and unchangeable landscape on which several kinds of particles interact. The interactions between these particles explain the basic forces observed in nature.

Each theory has its limitations. General relativity cannot explain the nature and behavior of subatomic particles, while quantum mechanics cannot explain gravitational forces.

Neither theory can explain everything seen in nature.

“Newton thought he had it, and then Einstein came along and made a tiny little adjustment, but intellectually it was huge,� said physicist Jim Faller, who participated in the first lunar ranging experiments.

“And if one ever found something wrong with the general theory of relativity . . . that would have the same impact that going from Newton to Einstein would have had.�

Some observations suggest problems with Einstein's theory, Murphy explained. General relativity's incompatibility with quantum mechanics is one. The theory also cannot explain why the universe is expanding at an accelerating rate.

“There are a number of pieces of evidence that suggest that general relativity isn't the final answer to gravity,� he said.

Laser force

Testing the effects of gravity in a conventional science lab is extremely difficult, because the gravitational forces exerted by objects of any manageable size are so weak. “When's the last time you saw two bowling balls attract each other gravitationally?� Murphy asked.

So, physicists look up.

“We have this gigantic, magnificent laboratory in the solar system, because we've got very large masses with very evident and strong attractions that give us a real strong handle on measuring gravity.�

Murphy's lunar ranging project, aptly named Apollo, combines a 3.5-meter telescope, the latest laser technology and a sophisticated light detector. Beginning in April and continuing six times a month, Murphy and his team fire pulses of light onto a telescope mirror and up into space.

The moon reflectors make a tiny target, and much of the light signal is lost by the time it returns to Earth. Meanwhile, both the Earth and the moon are moving in space, so astronomers have to shoot their laser slightly in front of their target and then look behind them for the return signal. They can't see the reflectors, but they have the moon coordinates so they know where to look. The telescope is essentially used as a big laser pointer.

The trip to the moon and back is short – about 2.5 seconds. The math is easy enough. Light travels at 186,000 miles per second, and a round trip covers about 478,000 miles. By knowing the speed of light and tracking the time it takes to return, Murphy can determine the distance the light has traveled.

The pulse leaving the telescope is approximately an inch thick and 10 feet in diameter, but the signal widens as it travels through Earth's atmosphere. That divergence stops growing when the pulse reaches the vacuum of space, but the angle of divergence continues all the way to the moon.

The result is that the pulses of laser light, by the time they reach the moon, cover a circular area of one to two miles across. If the reflectors are situated anywhere within that circle, at least some of the laser light will be reflected back to Earth.

The returning pulse of laser light continues to widen, so the photons that make it back to Earth cover an area about 10 miles in diameter. If the telescope mirror is anywhere within that circle of returning laser light, scientists should get a return signal.

Looking for photons

The signal is incredibly weak. Every pulse of laser light that leaves the telescope contains about 300,000,000,000,000,000 (300 quadrillion) photons of light. Scientists are happy when just one of those returns to their detector.

Here's another way to look at it: One out of every 30 million photons sent in a laser pulse will hit the lunar reflectors. And only one in 30 million of the reflected photons will be recaptured by the telescope at Apache Point.

“If you hit the reflector, it's like you just won the lottery – it's a one in 30 million chance,� Murphy said. “But imagine that you just won the lottery, and they tell you it's a one in 30 million chance the money will find it's way to your bank account.�

Of course, Murphy and his colleagues take steps to increase their chances. Each pulse contains a colossal number of photons, and they're shooting 20 pulses per second.

During the best of times, Murphy and his colleagues have gotten back about 2,500 photons in a 10-minute period. That may not seem like a lot, but it takes three years for the McDonald Observatory in Texas – the only other lunar ranging station in the country – to gather that many return photons, Murphy said.

More photons collected over a shorter period of time means that astronomers will be able to calculate the lunar orbit more quickly and with greater statistical accuracy. Repeated measurements are needed to build a picture of the lunar orbit over time.

The measurements are so precise that minuscule movements on Earth can skew the results. Pacific Ocean tides on the West Coast actually push against North America, depressing the crust in New Mexico – essentially lowering the ground. Other plate tectonic movements cause more complications.

To correct for these constant movements, Murphy's team uses a global positioning system station near Apache Point to monitor changes in elevations. Engineers are also developing an instrument called a superconducting gravimeter, which will be used to detect minute changes in surface gravity around Apache Point made by vertical movements in Earth's crust.

A year from now, Murphy and his colleagues may have enough information to begin a revolution in physics.

The prospect excites Faller, but it wouldn't necessarily surprise him.

“You're constantly looking under the rug, looking for dirt, and if you find some dirt, it's great,� he said. “It means there's something you don't really understand, and you didn't think about it correctly.�