What is relativity?
Special relativity
General relativity
Albert Einstein
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Apollo Lunar Laser Ranging

Neil Armstrong and Buzz Aldrin of Apollo 11 fame sparked off the lunar laser ranging experiments in 1969 when they installed a corner-cube prism (or retro-reflector) array on the surface of the Moon. Later, Apollo 14 and 15 installed two more retro-reflectors on different areas of the Moon. The Russian missions Luna 17 and 21 also ‘parked’ retro-reflectors on the Moon as part of the unmanned Lunokhod rovers.

The New Apollo

Over the years, the accuracy of laser ranging of the Moon has steadily increased to a (2005) best value of about 2 mm and in 2008 to about 1 mm. This is an incredibly small error over a distance averaging at 384000 km! Now there is a new measurement underway with a design aim of sub-millimeter errors – the objective is to be an order of magnitude better than previous measurements.

Apollo project telescope 'shooting' the Moon It is aptly named APOLLO, (for Apache Point Observatory Lunar Laser-ranging Operation), utilizing the 3.5-meter telescope at Apache Point in southern New Mexico. The photo shows part of the actual telescope 'shooting' the Moon with the laser. (Credit: Apollo project - click on picture for photos on Apollo website).

The purpose of the Apollo test is to enable scientists to gauge the relative acceleration of the Earth and Moon toward the Sun, or, as relativist Clifford Will stated it in his popular book (Was Einstein Right?) "do the Earth and the Moon fall the same?" This is an important test of Einstein’s theory of general relativity (gr). According to some theories of gravity competing with gr, the self-gravitation energy of massive bodies could make them fall differently. Such a test cannot be done in a laboratory, for obvious reasons.

The Challenge

Technically, the required accuracy for the Apollo test is very challenging. The type of laser used can produce high-energy pulses that are less than 100 picoseconds in duration, giving a pulse length of about 2.5 cm. Each pulse contains about 30 million million photons. Due to slight divergence of the laser beam and the small size of the reflectors, roughly one photon per pulse returns to the telescope after reflection from the retro-reflectors on the Moon. In previous experiments, only one photon per 100 pulses was detected.

Since it is not known where in the 2.5 cm long pulse the detected photon was, ranging errors are brought down to the sub-millimeter level by means of standard statistical techniques over many outgoing pulses and returning photons. Hence the importance of ‘catching’ as many photons per pulse as is possible.

A Moving Target

The apparent movement of the Moon relative to a point on Earth directly below the Moon is almost 100 000 km/h (the real relative movement is much smaller if the rotational offset is taken out). To hit a retro-reflector on the moon with a laser beam, one must aim the laser some 50 km ahead of the visual position of the reflector. The moon apparently moves about 25 km in the time the light from the moon takes to reach Earth. Then the Moon moves another 25 km while the laser’s photon bundle is on its way there.

To complicate things further, the exact same optics that sent the train of laser pulses to the Moon cannot be used to receive the echo. As explained above, the pulse optics must be slewed to always point at a spot some 50 km ahead of the reflector. By the time the echo is received back on Earth, the send optics no longer points in the direction that the echo is coming from.

A Moving Gun Platform

Another challenge is the fact that the surface of Earth is not at constant distance from its center. Tidal forces distort Earth’s crust by tens of centimeters and even tectonic plate movement and high/low pressure atmospheric systems have an effect on Earth’s shape. Once all these effects are compensated for, scientists believe they have the real distance between the centers of the Earth and the Moon.

The Moon has a pretty elliptical orbit and the distance varies from 365 000 km to 403 000 km. By accurately knowing the actual measured shape of the elliptical orbit, any deviations from the predictions of general relativity should stand out. If significant differences are ever found, Einstein’s theory of general relativity may be incomplete.

The Moon Drifting Away

Complicating the interpretation of the data is the fact that the Moon is presently receding from Earth at about 3.8 cm per year due to the tidal distortions it causes on Earth. The distortion of Earth’s crust is slowing down Earth’s rotation rate. The total angular momentum of the Earth-Moon system is however conserved by an increase in the Moon’s orbital energy – hence the gradual increase in the Moon’s average distance from Earth.

Due to Earth’s internal and tectonic movements, it is not easy to know exactly what portion of the change in Earth’s rotation rate is caused by the tidal effects. Consequently it is not perfectly clear what portion of the change in the Moon’s average distance is due to the tidal forces and what portion may be due to the sought after gravitational effects.

When Can We Expect Results?

The Apollo experiment is presently (mid 2006) in the ‘science run’ stage. The data analysis may take another six months or so. We may perhaps look forward to first results by the end of 2006.

[2008 Edit: 2006 and especially 2007 delivered good science results, achieving near 1 mm accuracies at times. Work is now concentrated on achieving sub-mm accuracies.]

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