The Lunar Laser Ranging Experiment

Abstract

The lunar ranging measurements now being made at the McDonald Observatory have an accuracy of 1 nsec in round-trip travel time. This corresponds to 15 cm in the one-way distance. The use of lasers with pulse-lengths of less than 1 nsec is expected to give an accuracy of 2 to 3 cm in the next few years. A new station is under construction in Hawaii, and additional stations in other countries are either in operation or under development. It is hoped that these stations will form the basis for a worldwide network to determine polar motion and earth rotation on a regular basis, and will assist in providing information about movement of the tectonic plates making up the earth's surface. Several mobile lunar ranging stations with telescopes having diameters of 1.0 m or less could, in the future, greatly extend the information obtainable about motions within and between the tectonic plates. The data obtained so far by the McDonald Observatory have been used to generate a new lunar ephemeris based on direct numerical integration of the equations of motion for the moon and planets. With this ephemeris, the range to the three Apollo retro-reflectors can be fit to an accuracy of 5 m by adjusting the differences in moments of inertia of the moon about its principal axes, the selenocentric coordinates of the reflectors, and the McDonald longitude. The accuracy of fitting the results is limited currently by errors of the order of an arc second in the angular orientation of the moon, as derived from the best available theory of how the moon rotates in response to the torques acting on it. Both a new calculation of the moon's orientation as a function of time based on direct numerical integration of the torque equations and a new analytic theory of the moon's orientation are expected to be available soon, and to improve considerably the accuracy of fitting the data. The accuracy already achieved routinely in lunar laser ranging represents a hundredfold improvement over any previously available knowledge of the distance to points on the lunar surface. Already, extremely complex structure has been observed in the lunar rotation and significant improvement has been achieved in our knowledge of lunar orbit. The selenocentric coordinates of the retroreflectors give improved reference points for use in lunar mapping, and new information on the lunar mass distribution has been obtained. Beyond the applications discussed in this article, however, the history of science shows many cases of previously unknown, phenomena discovered as a consequence of major improvements in the accuracy of measurements. It will be interesting to see whether this once again proves the case as we acquire an extended series of lunar distance observations with decimetric and then centimetric accuracy.

On the composition of the lunar interior

“…The presence of Ca rich garnet, perovskite, or corundum in the lower lunar mantle would serve to increase the density. The moment of inertia for the model as it stands is 0.391, in agreement with the new value 0.395 ± 0.005 [Bender et al, 1973].…”

“…The presence of Ca rich garnet, perovskite, or corundum in the lower lunar mantle would serve to increase the density. The moment of inertia for the model as it stands is 0.391, in agreement with the new value 0.395 ± 0.005 [Bender et al, 1973].Incompatible trace elements in the Apollo basalts at levels of 30-100 times higher than chondritic abundance levels suggested to Ringwood [1970] that maria were derived by a small degree of partial melting of volumes 30-100 times greater than their own, chondritic abundances in the source region being assumed. In contrast to this assumption Helmke et al [1972, 1973] propose that the common parent material for both the massive lunar anorthosites and the lunar basalts was about 14 times richer in REE than in chondrites.…”

The Apache Point Observatory Lunar Laser-ranging Operation: Instrument Description and First Detections

“…Other efforts in LLR are described in Williams et al (2005), and more detailed histories may be found in the preceding reference as well as in Bender et al (1973) and Dickey et al (1994).…”

“…These were performed on the 3.0 m telescope at the Lick Observatory. One month later, a second station using the 2.7 m telescope at the McDonald Observatory began ranging to the moon (Bender et al 1973). The operation at the Lick Observatory was designed for demonstration of initial acquisition, so that the scientifically relevant observations over the next decade came from the McDonald station, which used a ruby laser with 4 ns pulse width, firing at a repetition rate of about 0.3 Hz and ∼3 J pulse À1 .…”

The laser astrometric test of relativity mission

“…The PPN formalism has proved to be a versatile method to plan gravitational experiments in the solar system and to analyze the data obtained [7,8,27,28,29,30,31,32,33,34,35]. Different experiments test different combinations of these parameters (for more details, see [29]).…”