Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two... more Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even converted to an outer multipole with well established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three dimensional numerical integration of complex functions. Previous work has produced expressions for the low degree inner multipoles for certain elementary solids. This work goes further by presenting closed form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.
The close spacing between the proof mass and the housing in the LISA (Laser Interferometer Space ... more The close spacing between the proof mass and the housing in the LISA (Laser Interferometer Space Antenna) spacecraft has been a concern as there may be spurious feeble forces. Such forces may limit the performance of the gravity wave detector at frequencies below 3 mHz ...
A precise instrument, called a watt balance, compares mechanical power measured in terms of the m... more A precise instrument, called a watt balance, compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. We describe in this paper the fourth-generation watt balance at the National Institute of Standards and Technology (NIST), and report our initial determination of the Planck constant obtained from data taken in late 2015 and the beginning of 2016. A comprehensive analysis of the data and the associated uncertainties led to the SI value of the Planck constant, h = 6.626 069 83(22) × 10−34 J s. The relative standard uncertainty associated with this result is 34 × 10−9.
A new watt balance is being constructed at National Institute of Standards and Technology (NIST) ... more A new watt balance is being constructed at National Institute of Standards and Technology (NIST) in preparation for the redefinition of the International System of Units and the realization of mass through an exact value of the Planck constant. We describe the procedures used and give results for the measurements of the local acceleration of gravity in the new watt balance facility.
A redefinition of the International System of Units, the SI, is impending and could occur as earl... more A redefinition of the International System of Units, the SI, is impending and could occur as early as 2017. After redefinition, a means to realize the unit of mass is required. A watt balance is a promising device to realize the unit of mass at the kilogram level. At the National Institute of Standards and Technology (NIST), construction of a new watt balance with the sole purpose to realize mass is currently ongoing.
We report our recent investigations of the magnetization effect in the Kibble balance measurement... more We report our recent investigations of the magnetization effect in the Kibble balance measurement. It is confirmed by numerical studies that a diamagnetic force term linked to the current effect, which cannot be eliminated by mass-on and mass-off, should be contained in the weighing equations. Meanwhile, the same term is found in the velocity measurement, and hence it does not lead any considerable systematic errors in Kibble balance experiments.
Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two... more Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even converted to an outer multipole with well established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three dimensional numerical integration of complex functions. Previous work has produced expressions for the low degree inner multipoles for certain elementary solids. This work goes further by presenting closed form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.
The close spacing between the proof mass and the housing in the LISA (Laser Interferometer Space ... more The close spacing between the proof mass and the housing in the LISA (Laser Interferometer Space Antenna) spacecraft has been a concern as there may be spurious feeble forces. Such forces may limit the performance of the gravity wave detector at frequencies below 3 mHz ...
A precise instrument, called a watt balance, compares mechanical power measured in terms of the m... more A precise instrument, called a watt balance, compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. We describe in this paper the fourth-generation watt balance at the National Institute of Standards and Technology (NIST), and report our initial determination of the Planck constant obtained from data taken in late 2015 and the beginning of 2016. A comprehensive analysis of the data and the associated uncertainties led to the SI value of the Planck constant, h = 6.626 069 83(22) × 10−34 J s. The relative standard uncertainty associated with this result is 34 × 10−9.
A new watt balance is being constructed at National Institute of Standards and Technology (NIST) ... more A new watt balance is being constructed at National Institute of Standards and Technology (NIST) in preparation for the redefinition of the International System of Units and the realization of mass through an exact value of the Planck constant. We describe the procedures used and give results for the measurements of the local acceleration of gravity in the new watt balance facility.
A redefinition of the International System of Units, the SI, is impending and could occur as earl... more A redefinition of the International System of Units, the SI, is impending and could occur as early as 2017. After redefinition, a means to realize the unit of mass is required. A watt balance is a promising device to realize the unit of mass at the kilogram level. At the National Institute of Standards and Technology (NIST), construction of a new watt balance with the sole purpose to realize mass is currently ongoing.
We report our recent investigations of the magnetization effect in the Kibble balance measurement... more We report our recent investigations of the magnetization effect in the Kibble balance measurement. It is confirmed by numerical studies that a diamagnetic force term linked to the current effect, which cannot be eliminated by mass-on and mass-off, should be contained in the weighing equations. Meanwhile, the same term is found in the velocity measurement, and hence it does not lead any considerable systematic errors in Kibble balance experiments.
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