J. E. Faller

Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

On 21 July 1969, during the first manned lunar mission, Apollo 11, the first retroreflector array was placed on the moon, enabling highly accurate measurements of the Earthmoon separation by means of laser ranging. Lunar laser ranging (LLR) turns the Earthmoon system into a laboratory for a broad range of investigations, including astronomy, lunar science, gravitational physics, geodesy, and geodynamics. Contributions from LLR include the three-orders-of-magnitude improvement in accuracy in the lunar ephemeris, a several-orders-of-magnitude improvement in the measurement of the variations in the moons rotation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy. Lunar laser ranging analysis has provided measurements of the Earths precession, the moons tidal acceleration, and lunar rotational dissipation. These scientific results, current technological developments, and prospects for the future are discussed here.

A new generation of absolute gravimeters

We describe the design improvements incorporated in a new generation of absolute gravimeters, the FG5. A vertically oriented (in-line) interferometer design is used to remove the influence of floor vibration and tilt on the optical path length. The interferometer uses an iodine-stabilized laser as a primary length standard, with circuitry for automatic peak detection and locking. The seismic isolation system is an active long-period seismometer (Super Spring). The new design has improved passive isolation and thermal drift characteristics over previous systems. Programming flexibility and control of the test mass trajectory have been improved. The computer system has also improved real-time analysis and system capability. The FG5 instrument has a higher level of robustness, reliability and ease of use. These design advances have led to an instrumental uncertainty estimate of 1,1 × 10-8 m s-2 (1,0 μGal). Instrument agreement among nine similar devices is 1,8 μGal and observations under optimal conditions exhibit standard deviations of 5 μGal to 8 μGal.

The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information

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 earths 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 moons orientation as a function of time based on direct numerical integration of the torque equations and a new analytic theory of the moons 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.

Frequency stability measurements on polarization-stabilized He--Ne lasers

We present detailed stability measurements on six He-Ne lasers which have been stabilized by matching the intensity of the two orthogonal polarization modes. The frequencies of five different lasers were closely monitored for 1 month. Another laser was studied for 2 yr. All the lasers exhibited a stability of 1 part in 10(10) over the periods of about an hour and better than 1 part in 10(8) over 1 yr. An absolute accuracy of ~1 part in 10(9) can be attained by interpolating the linear drift between calibrations performed 6 months to 1 yr apart. These 1-mW lasers are rugged and simple to operate.

A Portable Apparatus for Absolute Measurements of the Earth's Gravity

We have developed a new and portable apparatus for making absolute measurements of the acceleration due to the Earths gravity. We use the method of free fall, and interferometrically determine the acceleration of a freely falling cube corner. In the design and development of this instrument, particular attention was paid to those aspects which would affect its performance in the field. The resulting instrument, we believe, provides a viable new tool for the study of tectonic motions. The system is very small; it can be transported in a small van and requires only two hours for assembly. A high rate of data acquisition is available; if necessary, a single measurement can be made every two seconds. Further, we have made a concerted effort to detect and (we hope) eliminate systematic errors. The results of extensive tests indicate that the achievable accuracy for g is about six parts in 109. This instrument therefore provides a sensitivity to vertical motions (e.g., of the Earths crust) as small as 2 cm.

Simple Pendulum Determination of the Gravitational Constant

We determined the Newtonian constant of gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672 34±0.000 14)×10(-11)  m3  kg(-1)  s(-2). This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value of (6.672 59±0.000 85)×10(-11)   m3  kg(-1)  s(-2) [Rev. Mod. Phys. 59, 1121 (1987)] but differs from some more recent determinations as well as the latest CODATA recommendation of (6.674 28±0.000 67)×10(-11)   m3  kg(-1)  s(-2) [Rev. Mod. Phys. 80, 633 (2008)].

Quadruple suspension design for Advanced LIGO

In this paper, we describe the conceptual design for the suspension system for the test masses for Advanced LIGO, the planned upgrade to LIGO, the US laser interferometric gravitational-wave observatory. The design is based on the triple pendulum design developed for GEO 600—the German/UK interferometric gravitational wave detector. The GEO design incorporates fused silica fibres of circular cross-section attached to the fused silica mirror (test mass) in the lowest pendulum stage, in order to minimize the thermal noise from the pendulum modes. The damping of the low-frequency modes of the triple pendulum is achieved by using co-located sensors and actuators at the highest mass of the triple pendulum. Another feature of the design is that global control forces acting on the mirrors, used to maintain the output of th ei nterferometer on a dark fringe, are applied via a triple reaction pendulum, so that these forces can be implemented via a seismically isolated platform. These techniques have been extended to meet the more stringent noise levels planned for in Advanced LIGO. In particular, the Advanced LIGO baseline design requires a quadruple pendulum with afi nal stage consisting of a 40 kg sapphire mirror, suspended on fused silica ribbons or fibres. The design is chosen to aim to reach a target noise contribution from the suspension corresponding to a displacement sensitivity of 10 −19 mH z −1/2 at 10 Hz at each of the tes tm asses. PACS number: 0480N

Results of the Sixth International Comparison of Absolute Gravimeters, ICAG-2001

Like all the previous International Comparisons of Absolute Gravimeters (ICAGs) the sixth, ICAG-2001, was held at the Bureau International des Poids et Mesures (BIPM). Major improvements in the 2001 campaign were a new measurement strategy using the absolute gravimeters to measure the ties of the gravity network, new sites constructed at the BIPM, improved relative measurements of the ties and gravity gradients, and combined adjustment of the absolute and relative data, realized using new software with a novel data weighting and rejection scheme. The g-values at four sites of the BIPM were measured with an uncertainty of 6 μGal. Good agreement was obtained between the results of the absolute and relative measurements of the ties of the gravity network. The final mean gvalue obtained at the reference site A was 7 μGal less than that obtained in the previous comparison, ICAG-97.

g-the acceleration of gravity: its measurement and its importance

The measurement of the acceleration of gravity (g) has long been a matter of scientific interest. Its value is of interest in a broad area of physical sciences, namely metrology, geophysics and geodesy. The authors discuss the various types of instrument, the methods of measurement and the applications of g.

Thirty years of progress in absolute gravimetry: a scientific capability implemented by technological advances

The application of technological advances has dramatically improved our ability to measure the absolute value of g, the free-fall acceleration due to gravity. Over the past thirty years this improvement has been nearly three orders of magnitude! Today, the value of gcan be determined with an accuracy approaching 1 µGal (10-8 m/s2) and measured with a precision that is at least ten times better. This paper reviews the history of and the reasons for this progress as well as taking a look to the future.