Was Galileo Wrong? - Galileo Galilei

A violation of the Equivalence Principle would reveal itself as a skewing of the Moon's orbit, either toward or away from the Sun. "Using masses as large as the Earth and Moon, we may be able to show this subtle effect, if it exists," notes Williams.

Scientists have been pinging the Moon since the Apollo days. So far, Einstein's theory of gravity - and the Equivalence Principle - has held up to a precision of a few parts in 10¹³. But that's not good enough to test all the theories vying to overthrow Einstein.

Current lunar laser ranging can measure the distance to the Moon - roughly 385,000 km - with an error of about 1.7 cm. Beginning this fall, a new facility funded by NASA and the National Science Foundation will boost this accuracy 10-fold to within only 1 to 2 mm. This jump in accuracy will mean that scientists can detect deviations from Einstein's theory 10 times smaller than currently possible, which may be sensitive enough to find the first evidence of flaws.

To achieve that accuracy, the facility, called the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO), must time the laser pulses' roundtrip flight to the Moon within a few pico seconds, or just a trillionth of a second (10^-12). The speed of light is known - it's about 300,000 km per second - so measuring the time of flight for the laser pulse tells scientists the distance between the APOLLO telescope and the mirror sitting on the surface of the Moon.

more A retro reflector array left on the Moon by Apollo 14 astronauts. Similar mirrors were emplaced by Apollo 11 and Apollo 15 astronauts, and by a pair of Soviet-era Lunokhod rovers.

How does APOLLO's design achieve this 10-fold improvement? First of all, it uses a larger telescope than the older facility at the McDonald Observatory in Texas - 3.5 meters vs. 0.72 meters. The larger mirror lets the APOLLO facility catch more of the photons of light returning from the Moon, explains Tom Murphy, a professor at the University of California, San Diego, and the mastermind behind the design of APOLLO. The smaller telescope catches, on average, only one returning photon for every 100 out-going laser pulses (each pulse contains more than 10¹⁷ photons!); the APOLLO telescope will catch about 5 photons from each pulse, which greatly improves the statistical strength of the results.