On the modelling and testing of a laboratory-scale Foucault pendulum as a precursor for the design of a high-performance measurement instrument.

An integrated study is presented on the dynamic modelling and experimental testing of a mid-length Foucault pendulum with the aim of confirming insights from the literature on the reliable operation of this device and setting markers for future research in which the pendulum may be used for the measurement of relativistic effects due to terrestrial gravity. A tractable nonlinear mathematical model is derived for the dynamics of a practical laboratory Foucault pendulum and its performance with and without parametric excitation, and with coupling to long-axis torsion is investigated numerically for different geographical locations. An experimental pendulum is also tested, with and without parametric excitation, and it is shown that the model closely predicts the general precessional performance of the pendulum, for the case of applied parametric excitation of the length, when responding to the Newtonian rotation of the Earth.

Erratum: Simple Pendulum Determination of the Gravitational Constant [Phys. Rev. Lett. 105, 110801 (2010)].

This corrects the article DOI: 10.1103/PhysRevLett.105.

Precision measurement, scientific personalities and error budgets: the sine quibus non for big G determinations.

Determinations of the Newtonian constant of gravitation (big G) fit into the oftentimes-unappreciated area of physics called precision measurement-an area which includes precision measurements, null experiments and determinations of the fundamental constants. The determination of big G-a measurement which on the surface appears deceptively simple-continues to be one of Nature's greatest challenges to the skills and cunning of experimental physicists. In spite of the fact that, on the scale of the Universe, big G's effects are so large as to single-handedly hold everything together, on the scale of an individual research laboratory, big G's effects are so small that they go unnoticed…hidden in a background of much larger forces and noise sources.

A simple pendulum laser interferometer for determining the gravitational constant.

We present a detailed account of our 2004 experiment to measure the Newtonian constant of gravitation with a suspended laser interferometer. The apparatus consists of two simple pendulums hanging from a common support. Each pendulum has a length of 72 cm and their separation is 34 cm.

Investigation of the Young's modulus and thermal expansion of amorphous titania-doped tantala films.

The current generation of advanced gravitational wave detectors utilize titania-doped tantala/silica multilayer stacks for their mirror coatings. The properties of the low-refractive-index silica are well known; however, in the absence of detailed direct measurements, the material parameters of Young's modulus and coefficient of thermal expansion (CTE) of the high refractive index material, titania-doped tantala, have been assumed to be equal to values measured for pure tantala coatings. In order to ascertain the true values necessary for thermal noise calculations, we have undertaken measurements of Young's modulus and CTE through the use of nanoindentation and thermal-bending measurements.

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.

The Measurement of Little g: A Fertile Ground for Precision Measurement Science.

The occasion of the 100th anniversary of Einstein's "golden year" provides a wonderful opportunity to discuss some aspects of gravity-gravitation being an interest of Einstein's that occurred a few years after 1905. I'll do this by talking about the measurement of little g, the free-fall acceleration on the Earth's surface that is mainly due to the Earth's gravity but whose value is also affected by centrifugal forces that are a result of the Earth's rotation. I will also describe two equivalence experiments and a test of the inverse-square law of gravitation.

A free-fall determination of the newtonian constant of gravity.

Recent determinations of the Newtonian constant of gravity have produced values that differ by nearly 40 times their individual error estimates (more than 0.5%). In an attempt to help resolve this situation, an experiment that uses the gravity field of a one-half metric ton source mass to perturb the trajectory of a free-falling mass and laser interferometry to track the falling object was performed.

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 moon's rotation, and the verification of the principle of equivalence for massive bodies with unprecedented 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.

Earth rotation measured by lunar laser ranging.

The estimated median accuracy of 194 single-day determinations of the earth's angular position in space is 0.7 millisecond (0.01 arc second).

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.

Laser ranging retro-reflector: continuing measurements and expected results.

After successful acquisition in August of reflected ruby laser pulses from the Apollo 11 laser ranging retro-reflector (LRRR) with the telescopes at the Lick and McDonald observatories, repeated measurements of the round-trip travel time of light have been made from the McDonald Observatory in September with an equivalent range precision of +/-2.5 meters. These acquisition period observations demonstrated the performance of the LRRR through lunar night and during sunlit conditions on the moon.