A vector field approach to calculating gravitational forces

Stirling, Julian

doi:10.1088/1367-2630/aa7c80

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Different densities will be given for different materials in these parts. Although there are some other more effective methods that could be used to do this calculation [25,26], the method used in this work is well implemented and sufficient for our current requirements, which will be discussed in 3.4.…”

Section: The Attraction Of the Apparatusmentioning

confidence: 99%

The self-attraction effect in an atom gravity gradiometer

Zhang¹,

Mao²,

Luo³

et al. 2020

Metrologia

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The selfattraction effect (SAE) is an important systematic error in a highprecision atom interferometry gravimeter, which has been researched. In this paper, we use the finite element method (FEM) to calculate the SAE of an atom gravity gradiometer. In this way, the SAE of the gravity gradiometer is accurately determined, and the calculation result shows this effect is 235(8) E (1 E = 1×10 −9 s −2 ) in the atom gravity gradiometer. Based on this calculation, this effect in many highprecision experiments can be corrected.

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Section: The Attraction Of the Apparatusmentioning

confidence: 99%

The self-attraction effect in an atom gravity gradiometer

Zhang¹,

Mao²,

Luo³

et al. 2020

Metrologia

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“…Computation of gravitational fields, forces, and torques can be accomplished by calculating sextuple integrals over the volumes of mass pairs, and summing for all pairs of source and test masses. Even with advanced methods to reduce these sextuple integrals to quadruple integrals [1,2], for certain elementary solids, this is extremely computationally intensive, especially considering that for many measurements this needs to be entirely recalculated for multiple source mass positions. More efficient methods are available for systems with favourable symmetries [3,4].…”

Section: Introductionmentioning

confidence: 99%

Closed form expressions for gravitational multipole moments of elementary solids

Stirling¹,

Schlamminger²

2019

Phys. Rev. D

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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. *

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“…The last two years have been used to accumulate experimental data without a new final report about the value of Big G. This is notable as there is limited research on this scientific concern in the present literature. Only some theoretical work as the produced by Stirling [2] shows a meticulous revision of the practical equation about gravitational interactions.…”

Section: Introductionmentioning

confidence: 99%

Toward a Common Ground for Gravity and Optics

Parra¹

2018

JAMP

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A long enough period of observation of the Sun's gravitational dragging effects by using a modified Cavendish's balance output of experimental evidence shows new patterns. Those patterns can be explained assuming that the Sun has a torus with rotation, precession, and nutation. This purpose of this paper is to introduce the frequencies of all those movements. The torus's rotational period can be used to explain the Sun's magnetic pole reversal. Utilizing a modified Cavendish's balance showed an output of dragging forces stronger than the attraction between the gravitational masses. This tool afforded this research a new experimental possibility to a more precise determination of the Universal Gravitational Constant Big G. Moreover, the dragging forces directly affect any volume of mass, which includes the atmosphere. This paper shows a correlation between the Sun's dragging peaks and density of the air squared. The aforementioned correlation and the inverse cubic relation with the distance to the Sun are common for the dragging and tide forces providing the possibility that tidal forces are also a gravitational dragging consequence. The last 2017 total Solar eclipse created a new temporal reaction on the modified Cavendish's balance. That temporal pattern looks as the spatial pattern created by an opaque disk. This similarity allows the researcher to calculate that the dragging forces are transmitted by photons with spatial periodicity of value λ = 6.1 km.

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A vector field approach to calculating gravitational forces

Cited by 4 publications

References 11 publications

The self-attraction effect in an atom gravity gradiometer

The self-attraction effect in an atom gravity gradiometer

Closed form expressions for gravitational multipole moments of elementary solids

Toward a Common Ground for Gravity and Optics

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