The Apache Point Observatory Lunar Laser-ranging Operation, or APOLLO, is a project at the Apache Point Observatory in New Mexico. It is an extension and advancement of previous Lunar Laser Ranging experiments, which use retroreflectors on the Moon to track changes in lunar orbital distance and motion.
Using telescopes on Earth, the reflectors on the Moon, and accurate timing of laser pulses, scientists were able to measure and predict the orbit of the Moon to a precision of a few centimeters by the early 2000s. This precision provides the best known test of many aspects of our theories of gravity. APOLLO improves this precision even further, measuring the distance between the Moon and Earth to within a few millimeters. Using this information, scientists will be able to further test various aspects of gravity, such as: determining whether the Earth and the Moon react the same to gravity despite their different compositions, investigating the predictions of Einstein with respect to the energy content of the Earth and the Moon and how they react to gravity, and evaluating whether general relativity correctly predicts the motion of the Moon.
The APOLLO collaboration built their apparatus on the 3.5 meter telescope at Apache Point in southern New Mexico. By using a large telescope at a site with good atmospheric seeing, the APOLLO collaboration gets much stronger reflections than any existing facilities. APOLLO records approximately one returned laser photon per pulse, as opposed to the roughly 0.01 photon-per-pulse average experienced by previous LLR facilities. The stronger return signal from APOLLO translates to much more accurate measurements.
History and motivation
High precision Lunar Laser Ranging (LLR) started soon after the Apollo 11 astronauts left the first retroreflector on the Moon. Additional reflectors were left by the Apollo 14 and Apollo 15 astronauts, and two French-built reflector arrays were placed on the Moon by the Soviet Luna 17 (Lunokhod 1) and Luna 21 (Lunokhod 2) lunar rover missions. Over the years since, many groups and experiments have used this technique to study the behavior of the Earth–Moon system, investigating gravitational and other effects.
For the first few years of the Lunar Laser Ranging Experiment, the distance between the observatory and the reflectors could be measured to an accuracy of about . Improved techniques and equipment lead to accuracies of until about 1984. Then McDonald Observatory built a special purpose system (MLRS) just for ranging, and achieved accuracies of roughly in the mid-to-late 1980s. In the early 1990s a French LLR system at the Observatoire de la Côte d'Azur (OCA) started operation, with similar precision.
The McDonald and OCA stations are collecting data that is about as good as possible, given the number of photons that they collect back from the reflectors. Although minor improvements are possible, getting significantly better data requires a larger telescope and a better site. This is the basic goal of the APOLLO collaboration.
The APOLLO laser has been operational since October 2005, and routinely achieves millimeter-level range accuracy between the Earth and the Moon.
Science goals
The goal of APOLLO is to push LLR into the millimeter range precision, which then translates directly into an order-of-magnitude improvement in the determination of fundamental physics parameters. Specifically, assuming improvements of a factor of ten over prior measurements, APOLLO will test: the Weak Equivalence Principle (WEP) to a part in , the Strong Equivalence Principle (SEP) to a few parts in , de Sitter relativistic precession to a few parts in , and the time variation of the gravitational constant G to a part in per year.
Tests of the Equivalence Principles
The Weak Equivalence Principle says that all objects fall the same way in a gravity field, no matter what they are made of. The Earth and the Moon have very different compositions—for example, the Earth has a large iron core, but the Moon does not. Furthermore, both are in orbit around the Sun, meaning that they are both falling towards the Sun at all times, even as they revolve around each other. If the Earth and the Moon were affected differently by the gravity of the Sun, this would directly affect the orbit of the Moon around the Earth. As closely as scientists can measure, the orbit of the Moon is just as predicted from assuming that gravity acts the same on each — to within 1 part in , the Earth and the Moon fall towards the Sun in exactly the same way, despite their different compositions. APOLLO will lead to even tighter limits.
The Strong Equivalence Principle, according to Albert Einstein's general relativity, predicts that the mass of any object consists of two parts – the mass of the atoms themselves, plus the mass of the energy that holds the object together. The question is whether the energy portion of mass contributes to measured gravity of the object, or to the inertia. In general relativity, the self-energy affects both the gravitational field and inertia, and does so equally.
Other modern theories, such as string theory, quintessence, and various forms of quantum gravity, almost all predict a violation of the Strong Equivalence Principle at some level. Additionally, many puzzling experimental results, such as galaxy rotation curves that imply the existence of dark matter or supernova observations that imply the existence of dark energy, could also potentially be explained by alternative theories of gravity (see, for example, MOND). Therefore, experimentalists believe it is important to make the most precise measurements of gravity possible, looking for any possible anomalies or confirming Einstein's predictions.
Precise ranging to the Moon can test the SEP since the Earth and the Moon have a different fraction of their mass in the energy component. Precision measurements are needed since this component is very small – if mE is the self energy of the Earth — the energy needed to spread the atoms of the Earth out to infinity against the attraction of gravity — then the mass of the Earth is by about mE/c = of the Earth's total mass. The self energy of the Moon is smaller yet, about of its mass. (The contribution for any object of laboratory size is negligible, about , so only measurements of planet-sized or bigger objects would allow this effect to be measured.), section 3.6.
If the Moon revolved around only the Earth, there would be no way to tell what fraction of the Moon's or the Earth's gravity was caused by each form of mass, since only the total can be measured. However, the orbit of the Moon is also strongly affected by the gravity of the Sun – in essence, Earth and Moon are in free fall around the Sun. If the energy portion of mass behaves differently from the conventional portion, then the Earth and the Moon will fall differently toward the Sun, and the orbit of the Moon around the Earth will be affected. For example, suppose the energy part of the mass does affect gravity, but does not affect inertia. Then: From our perspective on Earth, this would appear as a displacement, or polarization, of the lunar orbit away from the Sun with an amplitude of 13 meters. If the violation went the other way, with the self energy possessing inertial mass but not gravitational mass, the lunar orbit would appear to be polarized toward the Sun by the same amplitude. The calculation of the amplitude is complicated, but a crude estimate may be derived by multiplying the Earth's orbital radius of by the contribution to the Earth's mass from the self-energy to yield 75 meters.
The signature of an EP violation is very simple, depending only on the distance of the Moon from the Sun. This repeats about every 29.5 days, somewhat longer than the time the Moon takes to go around the Earth once, which is 27.3 days. (This difference arises since the Earth moves along its orbit as the Moon goes around, so the Moon has to make a little more than one orbit to get back to the same position relative to the Sun.) This makes EP particularly easy to measure, since many confounding effects such as tides or weather will not repeat at 29.5-day intervals. Unfortunately, there is one effect – radiation pressure acting on the orbit of the Moon – that does repeat each 29.5 days. Fortunately, it is small, less than 4 mm, and fairly easy to model, which allows it to be subtracted out.
Finally, even if the experiments show no effect, there is a tiny theoretical loophole. The measurements show the sum of the WEP and SEP violations. If the experiments show no effect, the most natural explanation is that neither WEP or SEP are violated. But it is conceptually possible that both are violated, and by equal and opposite amounts. This would be an incredible coincidence since WEP and SEP depend on very different and arbitrary properties – the exact composition of the Earth and the Moon, and their self-energies. But this unlikely case cannot be completely ruled out until either other solar system bodies are measured to similar precision, or laboratory experiments reduce the bounds on WEP violations alone.
Variations in the gravitational constant Existing ranging experiments can measure the constancy of the gravitational constant, G, to about one part in per year. The expansion rate of the universe is approximately one part in per year. So if G scaled with the size or expansion of the universe, existing experiments would already have seen this variation. This result can also be viewed as experimental verification of the theoretical result that gravitationally bound systems do not partake in the general expansion of the universe. APOLLO will place much tighter bounds on any such variations.
Other tests At this level of accuracy, general relativity is needed to predict the orbit of the Moon. Current tests measure geodetic precession to a 0.35% level of precision, gravitomagnetism at the 0.1% level, and checks whether gravity behaves as 1/r as expected. APOLLO will improve on all these measurements.
Principles of operation
APOLLO is based on measuring the time-of-flight of a short-pulse laser reflected from a distant target—in this case the retroreflector arrays on the Moon. Each burst of light lasts 100 picoseconds (ps). One millimeter in range corresponds to only 6.7 ps of round-trip travel time. However, the retroreflectors on the Moon introduce more than one millimeter of error themselves. They are not usually at an exact right angle to the incoming beam, so the different corner cubes of the retroreflectors are at different distances from the transmitter. This is because the Moon, although it keeps one face to the Earth, does not do so exactly—it wobbles from side to side and up and down, by as much as 10° in magnitude. (See libration.) These librations occur since the Moon rotates at constant speed, but has an elliptical and inclined orbit. This effect may seem small, but it is not only measurable, it forms the largest unknown in finding the range, since there is no way to tell which corner cube reflected each photon. The biggest array, the Apollo 15 reflector, can have a corner-to-corner range spread of ≈ 1.2 sin (10°) m, or 210 mm, or about 1.4 ns of round-trip time. The root-mean-square (RMS) range spread is then about 400 ps. To determine the distance to the reflector to 1 mm precision, or 7 ps, by averaging, the measurement needs at least (400/7)2 ≈ 3000 photons. This explains why a much larger system is needed to improve the existing measurements—the pre-APOLLO 2 cm RMS range precision required only about 10 photons, even at the worst-case orientation of the retroreflector array.