1 Introduction

On July 20, 1969, humans landed on the Moon for the first time. The following day, the Apollo 11 astronauts deployed the first Laser Ranging Retroreflector (LRRR or LR3). Within a month, return photons were successfully detected at several observatories [7]. Two more retroreflector arrays were placed on the Moon during the Apollo 14 and 15 missions. In addition, two French arrays were on Russian Lunokhod rovers carried on Luna landers. These five retroreflector arrays remain visible today and the laser ranging data collected over the past 40 years has dramatically and continually increased our understanding of gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics. They remain the only operating lunar experiment from the Apollo era, and more incredibly, only recently has the ground station technology advanced to the point where uncertainties associated with the lunar arrays are limiting the range measurement precision.

The Apollo 11 and 14 arrays consist of 100 fused silica ‘circular opening’ cubes (3.8 cm diameter each) with a total estimated lidar cross section (based on the intensity of the diffraction pattern of the array at the position of the receiver in the far field) of 0.5 billion square meters. Apollo 15 has 300 of these cubes and therefore about 3 times the lidar cross section and is the lunar array with the highest response. The diffraction pattern of the Apollo arrays has a bright central lobe at the center with six surrounding lobes with an effective tophat function 8 arcsec in diameter for small incidence angles [3, 40]. They produce an approximately 20 km diameter spot on Earth [24]. This spread is sufficient to cover the velocity aberration due to the Moon’s motion, so the cube’s reflective face angles were not intentionally spoiled (made different from 90 degrees).

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Figure 1: From left to right, the Apollo 11, 14, and 15 retroreflector arrays. (Image credits: NASA.)

The two Lunokhod arrays consist of 14 triangular shaped cubes, each side 11 cm. Shortly after landing, the Lunokhod 1 array ceased to be a viable target. However, in March 2010, it was located by NASA’s Lunar Reconnaissance Observer. Lunokhod 1 has now become a strong target for laser ranging, contrary to Lunokhod  2, which is very difficult to get returns from during the lunar day [44Jump To The Next Citation Point]. The silver rear coating and larger size of the Lunokhod cubes makes them less thermally stable, which dramatically reduces the optical performance when sunlit.

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Figure 2: The Russian Lunokhod 1 lander with the French built retroreflector array sticking out the left side. (Image credits: Lavochkin Association / NASA.)

Lunar laser ranging (LLR) is performed by measuring the round-trip light travel time between a ground transmitter and the retroreflector. Early LLR measurements had a precision of about 20 cm. Since 1969, multiple stations have successfully ranged to the lunar retroreflectors. However, two stations have dominated LLR data generation: McDonald Laser Ranging System (MLRS) in Texas (since 1969) [65] and Observatoire de la Côte d’Azur (OCA) in Grasse, France (since 1985) [59]. The vast majority of their lunar data comes from the array with the highest lidar cross section: Apollo 15. These stations have increased the range precision by a factor of 10 over the years to the level of about two centimeters. Recently, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has begun contributing high-quality data at the millimeter level [6Jump To The Next Citation Point, 42, 43Jump To The Next Citation Point].

Poor detection rates are a major limiting factor in past LLR. Taking into account velocity aberrations, optical performance of the ground station, and other systematic effects, the overall round-trip loss is typically of order 10–21, mostly due to the r4 loss from the Earth-Moon distance. Because of this heavy loss of light, not every laser pulse sent to the Moon results in a detected return photon, leading to poor measurement statistics. MLRS typically collects less than 100 photons per range measurement with a scatter of about 2 cm. However, the new APOLLO instrument at Apache Point has overcome this limitation.

The large collecting area of the Apache Point 3.5 m diameter telescope and the efficient avalanche photodiode arrays used in APOLLO result in thousands of detections (even multiple detections per pulse) leading to a statistical uncertainty of about 1 mm. The dominant random uncertainty per photon in APOLLO stems from the orientation of the reflector array and the associated spread of pulse return times [6Jump To The Next Citation Point]. Additionally, systematic errors associated with lunar arrays, such as regolith motion and thermal expansion of the array, start to become significant at the millimeter level of precision.

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Figure 3: Improvements in the ground station technology over the past 40 years have increased the range precision by 2 orders of magnitude. Uncertainties associated with the existing retroreflectors are now becoming a limitation. (Image credits: Thomas Murphy.)

Each ground station records the single-photon reflection events, which are then combined into ‘normal points’ that are adjusted for station-specific corrections. A typical normal point is generated from 5 to 20 minutes of ranging. The normal points are then submitted to a central archive with the International Laser Ranging Service [58Jump To The Next Citation Point], which makes them available to the public. Auxiliary measurements, such as environmental conditions (temperature, pressure, etc.) are also recorded, as these are required to further correct the data for atmospheric effects. A detailed model of the solar system ephemeris is then used to perform a least-squares analysis to estimate various model parameters from the measured data [80Jump To The Next Citation Point].

Arguably, the most fruitful analysis of LLR data is for tests of General Relativity (GR). Relativistic effects typically show up at particular frequencies (such as the synodic frequency) making them separable from most other parameters. These frequency signatures make the analysis possible given the plethora of other effects with large uncertainties. In the following sections, we summarize the main tests of GR performed with LLR. These include tests of the Equivalence Principle, the variation of the gravitational constant, the inverse square law, and a preferred-frame. We then discuss the current state of LLR data analysis. Finally, we describe the next generation of lunar laser ranging instruments and discuss the possibilities that the future of lunar and planetary laser ranging may hold.

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