Anthonares

While most folks remember Apollo for the videos and photos it returned of a foreign, desolate world, some of the science experiments left behind have gone under-appreciated. Two of the science experiments, the Lunar Laser Ranging Experiment and the lunar seismometers (Passive Seismic Experiments), returned data long after the astronauts left. While the lunar seismometers were turned off in 1977, the Lunar Laser Ranging Experiment (LLRE) continues to this day, and has produced some incredible results. For instance, we now know that the Moon still has a liquid core, that the fundamental gravitational constant G is either static or is evolving very very slowly, that Einstein’s General Theory of Relativity predicts the Moon’s orbit better than we can measure it, and that the Moon is receding from us at a rate of about 3.8 cm/year.

The primary reason that the LLRE has been so successful is that it is allows for almost unlimited upgradeability in precision, is free to use, and costs no money to maintain. In the 35 years since the first LLRE reflector was deployed by the Apollo 11 astronauts, dozens of teams have used the laser reflectors to learn more about lunar geology and the evolution of the Earth/Moon system, as well as to conduct basic physics research. Scientists continue to use the LLRE reflectors today and are constantly improving their accuracy so that in the coming years new research can be conducted with these astounding little experiments.

The LLRE

One retro-reflectors was positioned on the surface of the Moon during each of the Apollo 11, 14, and 15 missions (two additional reflectors were carried on the Soviet missions Lunakhod 1 and 2, though Lunakhod 1’s reflector has never returned any data). Here is an image showing the approximate locations of each reflector. These retro-reflectors consist of corner-cube quartz crystals that are capable of returning a light signal in the exact same direction from which it was received (see this diagram). The basic idea of this experiment is that scientists on Earth would direct a laser at these reflectors and then time how long it takes for that beam to return. Since the speed of light is constant, the distance to the moon is then given by this super-simple formula: distance = 1/2 * (travel time)/(speed of light, c).

But, while the principle is dead simple, the actual practice is quite a challenge. Scientists are not interested in the approximate distance to the moon, but rather the exact distance, or as near as can be obtained. To achieve an accuracy of about 1 cm, which is about 1 part in 5 billion of the total 385,000 km distance, the laser travel time has to be accurate to about 35 picoseconds (35*10^-12 seconds)! Not only that, but the targeting has to be incredibly precise. A laser beam that starts out from a telescope on earch at about 1 meter width slowly diverges and is blurred by the atmosphere until it is about 10 km wide on the surface of the moon. While that’s a pretty big beam, it’s still only a tiny fraction of the Moon’s surface, so all sorts of ridiculous analogies about the level of accuracy can be invented. For instance, it’s like a pigeon pooping directly into my coffee cup while flying at 35 km/hr at 32,000 feet (don’t check those numbers too closely, never mind the physical limitations on flying that high, suffice to say that it’s not an easy aim). The image on the right is courtesy the McDonald Observatory from their laser ranging facility.

The Science

So, the LLRE is definitely some gee-whiz engineering, but why should we care that we can measure the Earth-Moon distance so accurately? Well, as I alluded to above, the science return from this fascinating little set of experiments has been considerable. Knowing the distance to the moon very accurately tells us a number of things. But perhaps most interesting, to me at least, is the confirmation and exact measurement of the rate at which the moon is receding.

The Moon has the effect of pulling some of the mass of the Earth towards it, which we call tides. Because the Earth rotates much more quickly than the moon orbits, the mass of water and rock that the moon pulls towards then rotates out ahead of the moon. This increase in mass “in front” of the moon in its orbit pulls the moon forward, accelerating it. This then transfers rotational energy from the Earth into kinetic energy of the moon. The net effect is that the Earth’s rotation slows down and the moon’s orbit nudges slightly further away from the Earth.

Compared the distance between the Earth and the Moon, the rate of change in the Moon’s orbital distance is very small. The current measurement of the rate at which the moon is receding from the Earth is about 3.8 cm/year. But, years pass rather quickly over geologic time. Over a period of a billion years, this amounts to a change of about 10% in the Earth-Moon distance. Geologic records indicate that this recession rate is a bit high, and that a number more like 2 cm/year is a good average over the last few hundred million years (The story of how we can get this information from the rock record is pretty amazing. Some coral accumulate layers on both daily and yearly cycles, thus the length of the year during any given geologic period can be calculated fairly accurately).

While the moon used to be much closer to us than it is today, this means that, by conservation of angular momentum, the Earth had to rotate much more quickly. In fact, the length of a day when the moon first formed was probably about 6 hours, and by 600 million years ago had reached approximately 21.9 hours. The maximum length of the day will be reached when the Earth rotates at the same speed the moon orbits. In other words, the day and the month will have the exact same value, somewhere near 47 days. At this point, the moon will hang suspended above one hemisphere of the Earth and will disappear entirely from the sky for half of the world. But, relax, the sun will have gone out by then.

The more immediate benefit of the accurate Earth-Moon distances made possible by the LLRE is that scientists can calculate historical eclipses with great accuracy. This has made possible accurate dating of historical events that had been marked by notable eclipses. We also know that the total solar eclipse is a transient phenomenon. We happen to exist in the 1.5-2 billion year window in which both annual and total eclipses are possible. Approximately 800 million years ago, there were no annular eclipses, the moon was too close to the Earth to allow the sun to peek around its edges. But gradually, the relative frequency of annular eclipses has been increasing relative to total eclipses. And sometime about 1 billion years (there’s a lot of slop in this estimate) from now the last totality will occur. So see it while it lasts!