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

Modeling Development of a Diamagnetically Stabilized Magnetically Levitated Gravimeter

The aim of this work is to create a new type of gravimeter that can function effectively in the challenging conditions of space, specifically on the surfaces of planets and moons. The proposed device, called a diamagnetically stabilized magnetically levitated gravimeter (DSMLG), uses magnetic forces to balance a test mass against the force of gravity, allowing for accurate measurements. A diamagnetically stabilized levitation structure comprises a floating magnet, diamagnetic material, and a lifting magnet. The floating magnet levitates between two diamagnetic plates without the need for external energy input due to the interaction between the magnetic forces of the floating magnet and the stabilizing force of the diamagnetic material. This structure allows for stable levitation of the floating magnet without requiring additional energy. The goal is to design a gravimeter that is lightweight, requires minimal power, can withstand extreme temperatures and shocks, and has a low data rate. The authors envision this gravimeter being used on various robotic spacecraft, such as landers and rovers, to study the interiors of rocky and icy celestial bodies. This paper reports on the results of a finite element model analysis of the DSMLG and the strength of the resulting diamagnetic spring. The findings contribute to the understanding of the levitation characteristics of diamagnetically stabilized structures and provide valuable insights for their practical applications, including in the development of the proposed DSMLG.

The measurement of surface gravity

This review covers basic theory and techniques behind the use of ground-based gravimetry at the Earth's surface. The orientation is toward modern instrumentation, data processing and interpretation for observing surface, land-based, time-variable changes to the geopotential. The instrumentation side is covered in some detail, with specifications and performance of the most widely used models of the three main types: the absolute gravimeters (FG5, A10 from Micro-g LaCoste), superconducting gravimeters (OSG, iGrav from GWR instruments), and the new generation of spring instruments (Micro-g LaCoste gPhone, Scintrex CG5 and Burris ZLS). A wide range of applications is covered, with selected examples from tides and ocean loading, atmospheric effects on gravity, local and global hydrology, seismology and normal modes, long period and tectonics, volcanology, exploration gravimetry, and some examples of gravimetry connected to fundamental physics. We show that there are only a modest number of very large signals, i.e. hundreds of µGal (10(-8) m s(-2)), that are easy to see with all gravimeters (e.g. tides, volcanic eruptions, large earthquakes, seasonal hydrology). The majority of signals of interest are in the range 0.1-5.0 µGal and occur at a wide range of time scales (minutes to years) and spatial extent (a few meters to global). Here the competing effects require a careful combination of different gravimeter types and measurement strategies to efficiently characterize and distinguish the signals. Gravimeters are sophisticated instruments, with substantial up-front costs, and they place demands on the operators to maximize the results. Nevertheless their performance characteristics such as drift and precision have improved dramatically in recent years, and their data recording ability and ruggedness have seen similar advances. Many subtle signals are now routinely connected with known geophysical effects such as coseismic earthquake displacements, post-glacial rebound, local hydrological mass balances, and detection of non-steric sea level changes.

History and progress on accurate measurements of the Planck constant

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.