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The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect depends on the surface potentials through their spatial autocorrelation functions. By making some modification to the quasi-local correlation model, we obtain a rigorous formula for the patch force, where the magnitude is proportional to ${\frac{1}{{{a}^{2}}}{{(\frac{a}{w})}^{\beta (a/w)+2}}}$ with ${a}$ the distance between two parallel plates, ${w}$ the mean patch size, and ${\beta}$ the scaling coefficient from ${-2}$ to ${-4}$. A torsion balance experiment is then conducted, and obtain a 0.4 mm effective patch size and 20 mV potential variance. In the latter case, we apply an adatom diffusion model to describe this mechanism and predicts a ${f^{-3/4}}$ frequency dependence above 0.01 ${\rm mHz}$. This prediction meets well with a typical experimental results. Finally, we apply these models to analyze the patch effect for two typical experiments. Our analysis will help to investigate the properties of surface potentials.

Ethylene (C

ispartof: PETROLEUM SCIENCE vol:19 issue:6 pages:2631-2648 status: published

Highly selective separation and purification of acetylene (C2H2) from ethylene (C2H4) and carbon dioxide (CO2) are daunting challenges in light of their similar molecule sizes and physical properties. Herein, we report a two-dimensional (2D) stable metal–organic framework (MOF), NUM-11 ([Cu(Hmpba)2]·1.5DMF) (H2mpba = 4-(3,5-dimethyl-1H-pyrazol-4-yl)benzoic acid), with sql topology, stacked together through π–π interactions for efficient separation of C2H2 from C2H4 and CO2. The 2D-MOF material offers high hydrolytic stability and good purification capacity; especially, it could survive in water for 7 months, even longer. This stable MOF selectively captures C2H2 from mixtures containing C2H4 and CO2, as determined by adsorption isotherms. The ideal adsorbed solution theory selectivity calculations and transient breakthrough experiments were performed to verify the separation capacity. The low isosteric heat of NUM-11a (desolvated NUM-11) (18.24 kJ mol–1 for C2H2) validates the feasibility of adsorbent regeneration with low energy footprint consumption. Furthermore, Grand Canonical Monte Carlo simulations confirmed that the pore surface of the NUM-11 framework enabled preferential binding of C2H2 over C2H4 and CO2 via multiple C–H···O, C–H···π, and C–H···C interactions. This work provides some insights to prepare stable MOF materials toward the purification of C2H2, and the water-stable structure, low isosteric heat, and good cycling stability of NUM-11 make it very promising for practical industrial application.

The residual gas damping in the enclosure surrounding a free-fall test mass is an important limiting factor for the sensitivity of some space detection missions. We present a constrained volume damping model for space-borne gravitational wave detection, which depends on the escape time needed for a molecule to diffuse out of the gap between two adjacent surfaces. Using a completely inelastic molecular collision prediction, we calculate the escape times in the two most common constrained volumes, cylinder and cuboid, respectively. Both calculations agree well with Monte Carlo simulations. Additionally, the theoretical model of the residual gas damping presented in this work is in good agreement with the experimental results in the ground torsion pendulum test of LISA and its precursor LISA Pathfinder.

The separation of ethylene (C2H4) from C2 hydrocarbons is considered as one of the most difficult and important processes in the petrochemical industry. Heat-driven cryogenic distillation is still widely used in the C2 hydrocarbons separation realms, which is an energy intensive process and takes up immense space. In response to a greener, more energy-efficient sustainable development, we successfully synthesized a multifunction microporous Mg-based MOF [Mg2(TCPE)(µ2-OH2)(DMA)2].solvents (NUM-9) with C2H6/C2H2 selectivity based on a physical adsorption mechanism, and with outstanding stability; especially, it is stable up to 500 °C under an air atmosphere. NUM-9a (activated NUM-9) shows good performances in the separation of C2H6/C2H2 from raw ethylene gases. In addition, its actual separation potential is also examined by LAST and dynamic column breakthrough experiments. GCMC calculation results indicate that the unique structure of NUM-9a is primarily conducive to the selective adsorption of C2H6 and C2H2. More importantly, compared with C2H4, NUM-9a prefers to selectively adsorb C2H6 and C2H2 simultaneously, which makes NUM-9a as a sorbent have the capacity to separate C2H4 from C2 hydrocarbon mixtures under mild conditions through a greener and energy-efficient separation strategy.

5-Hydroxymethylfurfural (HMF) containing C=O, C-O, and furan ring functional groups is an important platform chemical derived from C

The propane (C3H8)-trapping adsorption behavior is considered as a potential performance to directly produce high-purity propylene (C3H6). Herein, we report an ultramicroporous Mn-based metal-organic framework (NUM-7) with a reverse C3H8-selective behavior in the low-pressure area. The pore structure of this material possesses more electronegative aromatic benzene rings for the stronger binding affinity to C3H8, and the material shows outstanding reverse ideal adsorbed solution theory (IAST) selectivity values. Single-component sorption isotherms preliminarily show the reverse adsorption behavior in the low-pressure part, and the moderate heat of adsorption further confirms this performance and exhibits less energy consumption for regeneration. In addition, the purification effect for the C3H8/C3H6 mixture is evaluated by the IAST selectivity and transient breakthrough curves, and the GCMC calculation results reveal that the fascinating C3H8-trapping behavior mainly depends on the multiple C-H···π interactions. Moreover, because C3H6 is the desired target product, the interesting C3H8-selective adsorption behavior of NUM-7 may provide its potential for one-step purification of C3H6, and this work can provide the method of developing C3H8-selective materials for the purification of C3H6.

Experiments measuring the Newtonian gravitational constant $G$ can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring $G$ is presented, which permits a test of the $1/{r}^{2}$ law at the centimeter range. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of Yukawa-type deviations from Newtonian gravity in the range of 5--500 mm and improves the previous bounds by up to a factor of 7 at the length range of 60--100 mm.

The TianQin Project is aiming at gravitational wave (GW) detection in space. TianQin GW observatory comprises three satellites orbiting on 1 × 105 km Earth orbits to form an equilateral-triangle constellation. In order to minimize the variations in arm lengths and breathing angles, the satellites must be launched and adjusted precisely into an optimized orbit. Therefore, satellite laser ranging must be used to enhance the precision of satellite orbit determination. To develop the capability of satellite laser ranging for TianQin’s orbit, the TianQin Laser Ranging Station has been designed and constructed to perform high-precision laser ranging for TianQin satellites and lunar laser ranging as well. Applying a 1064 nm Nd: YAG laser with 100 Hz repetition frequency, 80 pico-second pulse duration, and 2 × 2 array of superconducting nanowire single-photon detectors, we have obtained the laser echo signals from the five lunar retro-reflector arrays, and the measurement data have been packaged into 234 normal points (NPs), including a few data measured during the full-moon lunar phase. Each NP is calculated from continuous measurement for about ten minutes and the statistical error of the NPs is about 7 mm (1σ).

Short-range tests of the gravitational inverse-square law are very important for finding new interactions. In order to further improve the constraints on the Yukawa-like gravitational force, we propose a new scheme based on the torsion balance, where the speculative Yukawa-like gravitational force between the pendulum and the attractor is substantially increased by increasing the area of the test mass and the source mass. A dual-compensation design is used to realize a null experiment, which can release the accuracy requirement on some geometric parameters. The calculation result shows that, at the 95% confidence level, the new design can establish the strongest bound on the magnitude α of the Yukawa violation at the range of 40–800 μm with the total error of about 2.0 × 10−17 N m, and improve the previous bounds about one order of magnitude at the length scale λ ≈ 300 μm.

For the experiments of testing the Newtonian inverse-square law (ISL) at short range, we have analyzed the residual gas damping effect under the assumption of the temperature of the gas is isothermal (Ke J et al 2020 Class. Quantum. Grav. 37 205008). However, when the test mass squeezes the gas, the temperature of the gas will change accordingly and may cause additional noise. It is essential to study this phenomenon in pursuit of higher precision test of ISL. Here, we discuss the non-isothermal squeeze film damping by using the differential equations of energy conservation and change in molecular density. The results show that this kind of Brownian motion torque noise is larger than that estimated previously and is influenced by the degrees of freedom of molecules. Namely, a larger accessible distance between test bodies is needed in comparison to the internal damping of the pendulum.

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., 16 pages, 1 figure, invited article to a special section in PTEP

We report on an experimental test of the velocity and spin dependent exotic interaction that can be mediated by new light bosons. The interaction is searched by measuring the force between a gold sphere and a microfabricated magnetic structure using a cantilever. The magnetic structure consists of stripes with antiparallel electron spin polarization so that the exotic interaction between the polarized electrons in the magnetic structure and the unpolarized nucleons in the gold sphere varies periodically, which helps to suppress the spurious background signals. The experiment sets the strongest laboratory constraints on the coupling constant between electrons and nucleons at the micrometer range with f⊥ < 5.3 × 10−8 at λ ¼ 5 μm.

Capacitive transducers are widely used in fundamental physics experiments, seismology, Earth or planetary observations, and space scientific and technical applications because of their high precision, simple structure, and compatibility with various measurements. However, in real applications, there is a trade-off between their resolution and dynamic range. Therefore, this paper is aimed at enlarging the dynamic range while ensuring high resolution. In this paper, a noise analysis of a capacitive transducer is presented, which shows that the amplitude noise of the carrier wave is the main limiting factor. Hence, a new method of generating a carrier wave with lower-amplitude noise is proposed in the paper. Based on the experimental verification, it is found that the carrier wave produced through the new method performed significantly better than the typical digital carrier wave when they were compared in the same sensing circuit. With the carrier wave produced through the new method, the dynamic range of the capacitive transducer can reach 120.7 dB, which is 18.3 dB greater than for the typical direct digital synthesis (DDS) method. In addition, the resolution of the carrier wave is mainly limited by the voltage reference components.

As a new type of porous material, metal-organic frameworks (MOFs) have been widely studied in gas adsorption and separation, especially in C

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds ($|\ensuremath{\alpha}|\ensuremath{\le}1$) down to a length scale $\ensuremath{\lambda}=48\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of the Yukawa violation in the range of $40--350\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, and improves the previous bounds by up to a factor of 3 at the length scale $\ensuremath{\lambda}\ensuremath{\approx}70\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for $k=4$ and 5.

The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about $1\times10^{-10}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$ and about $5\times10^{-11}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.05~{\rm Hz}\,$, measured by an inertial sensor with a sensitivity of $5\times10^{-12}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The micro-Newton thrusters has demonstrated a thrust resolution of $0.1~\mu{\rm N}$ and a thrust noise of $0.3~\mu{\rm N}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}$. The residual noise of the satellite with drag-free control is $3\times10^{-9}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The noise level of the optical readout system is about $30~{\rm pm}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The temperature stability at temperature monitoring position is controlled to be about $\pm3~{\rm mK}$ per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than $0.1~{\rm mm}$., Comment: 17 pages, 11 figures

In this paper, we present a suppression method for the thermal drift of an ultra-stable laser interferometer. The detailed analysis on the Michelson interferometer indicates that the change in optical path length induced by temperature variation can be effectively reduced by choosing proper thickness and/or incident angle of a compensator. Taking the optical bench of the Laser Interferometer Space Antenna Pathfinder as an example, we analyze the optical bench model with a compensator and show that the temperature coefficient of this laser interferometer can be reduced down to 1 pm/K with an incident angle of 0.267828 rad. The method presented in this paper can be used in the design of ultra-stable laser interferometers, especially for space-based gravitational waves detection.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10−11 and 6.674484 × 10−11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

TianQin-1 is a mission in the TianQin project, which uses a single satellite to demonstrate the maturity of the key technology for the space-based gravitational wave detection. The spaceborne laser in the TianQin-1 mission consists of a self-developed DBR one and a commercial RIO one. The DBR laser is also developed as a pumping source for the main NPRO laser in the final solution of TianQin. The two lasers were mutual backups and both passed the environment performance verification. The on ground results showed that the self-developed DBR laser could provide a stable output of 18 mW with a drift of 0.6 mW/h. Meanwhile, the internal temperature was controlled at the mK level. The results of in-orbit experiments show that the DBR laser works well as a direct source of the laser interferometer. The overall displacement resolution and the noise floor of the interferometer was approximately 25 pm and 30 pm/√Hz at 0.1 Hz, respectively, better than the goals of the TianQin-1 mission.

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

Precision measurements of the inverse-square law via experiments on short-range gravity provide sensitive tests of Lorentz symmetry. A combined analysis of data from experiments at the Huazhong University of Science and Technology and Indiana University sets simultaneous limits on all 22 coefficients for Lorentz violation correcting the Newton force law as the inverse sixth power of distance. Results are consistent with no effect at the level of $10^{-12}$ m$^{4}$., 7 pages two-column REVTeX, accepted for publication in Physical Review Letters

Improving the precision of current tests of the equivalence principle with a rotating torsion pendulum requires a more complete analysis of systematic effects. Here, we discuss in detail one of the important systematic effects, the influence from the tilt error motion of the rotation axis of a rotary stage, namely, wandering of the instantaneous rotation axis around its average direction. Its influence on the rotating torsion pendulum is modeled phenomenologically, and the parameters in the model are calibrated. It is shown that the influence can contribute a correction of η ≈ 5 × 10−13 to the equivalence-principle violating parameter for a rotary stage whose tilt error motion of interest is about 31 nrad in magnitude. We also show that such an influence can be reduced to the level of η ≈ 1 × 10−14 by means of active compensation of the tilt error motion using a set of piezoelectric actuators placed under the stage stator.

Here we present a new test of the equivalence principle designed to search for the possible violation of gravitational parity using test bodies with different chiralities. The test bodies are a pair of left- and right-handed quartz crystals, whose gravitational acceleration difference is measured by a rotating torsion pendulum. The result shows that the acceleration difference towards Earth $\mathrm{\ensuremath{\Delta}}{a}_{\text{left}\text{-right}}=[\ensuremath{-}1.7\ifmmode\pm\else\textpm\fi{}4.1(\text{stat})\ifmmode\pm\else\textpm\fi{}4.4(\text{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{m}\text{ }{\mathrm{s}}^{\ensuremath{-}2}$ ($1\text{\ensuremath{-}}\ensuremath{\sigma}$ statistical uncertainty), correspondingly the E\"otv\"os parameter $\ensuremath{\eta}=[\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}2.8(\text{stat})\ifmmode\pm\else\textpm\fi{}3.0(\text{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$. This is the first reported experimental test of the equivalence principle for chiral masses and opens a new way to the search for the possible parity-violating gravitation.

The large spread in recent published $G$ values suggests that there may be some undiscovered systematic sources in these experiments. With the aim of identifying possible errors and obtaining a more reliable $G$ value, our group has performed two independent methods simultaneously. Besides the time-of-swing method which we have worked on for more than 20 years [1], [2], another determination of $G$ with the angular acceleration feedback method was carried out at the same laboratory. In the AAF method, two coaxial turntables are used to rotate the torsion pendulum and the source masses individually. With the help of a feedback control system [3], the torsion fiber does not twist by matching the rotating rate of the two turntables. As a result, this method is insensitive to the fiber's properties. In this work, several sources of uncertainty existed in our preliminary experiment [4] are reduced: (1) An ultra-low thermal expansion (ULE) glass shelfis used to support the source masses instead of the aluminium shelf to reduce the temperature influence on the distance between source masses; (2) The background gravity gradient of the rotating shelf is measured and compensated with small blocks so that its effect to the $G$ value is reduced to ~1 ppm; (3) Two different methods are used to check the source mass distance to improve the confidence level. With the improvements shown above and a lot of careful systematic error evaluation, a new $G$ value with a prospective uncertainty of less than 15 ppm will be obtained.

We have measured the Newtonian gravitational constant $G$ by using high-Q silica fibers with time-of-swing method. A series of improvements have been adopted to reduce the large corrections and uncertainties.

Recently, first limits on putative Lorentz invariance violation coefficients in the pure gravity sector were determined by the reanalysis of short-range gravity experiments. Such experiments search for new physics at sidereal frequencies. They are not, however, designed to optimize the signal strength of a Lorentz invariance violation force; in fact the Lorentz violating signal is suppressed in the planar test mass geometry employed in those experiments. We describe a short-range torsion pendulum experiment with enhanced sensitivity to possible Lorentz violating signals. A periodic, striped test mass geometry is used to augment the signal. Careful arrangement of the phases of the striped patterns on opposite ends of the pendulum further enhances the signal while simultaneously suppressing the Newtonian background., Accepted Phys. Rev. D

The authors of the paper [1], Grav. Cosmol. 16, 323 (2010), presented two methodologies for calculating the gravitational torque while measuring the gravitational constant G by a dynamic method. We have checked their calculations and found an evident error which directly leads a wrong conclusion in the paper. Besides, their discussion on the advantage of the methodology includes a logical contradiction.

The high precision test of the weak equivalence principle (WEP) using a rotating torsion pendulum requires thorough analysis of systematic effects. Here we investigate one of the main systematic effects, the coupling of the ambient magnetic field to the pendulum. It is shown that the dominant term, the interaction between the average magnetic field and the magnetic dipole of the pendulum, is decreased by a factor of 1.1 × 104 with multi-layer magnetic shield shells. The shield shells reduce the magnetic field to 1.9 × 10-9 T in the transverse direction so that the dipole-interaction limited WEP test is expected at η ≲ 10-14 for a pendulum dipole less than 10-9 A m2. The high-order effect, the coupling of the magnetic field gradient to the magnetic quadrupole of the pendulum, would also contribute to the systematic errors for a test precision down to η ∼ 10-14.

By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 μm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59 μm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300 μm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160 μm.

A search for sidereal variations in the non-Newtonian force between two tungsten plates separated at millimeter ranges sets experimental limits on Lorentz invariance violation involving quadratic couplings of Riemann curvature. We show that the Lorentz invariance violation force between two finite flat plates is dominated by the edge effects, which includes a suppression effect leading to lower limits than previous rough estimates. From this search, we determine the current best constraints of the Lorentz invariance violating coefficients at a level of $10^{-8}$ m$^{2}$., 5 pages, 3 figures. arXiv admin note: text overlap with arXiv:1412.8362 by other authors

Low frequency 1/f noise is one of the key limiting factors of high precision measurement instruments. In this paper, digital correlated double sampling is implemented to reduce the offset and low frequency 1/f noise of a data acquisition system with 24-bit sigma delta (Σ-Δ) analog to digital converter (ADC). The input voltage is modulated by cross-coupled switches, which are synchronized to the sampling clock, and converted into digital signal by ADC. By using a proper switch frequency, the unwanted parasitic signal frequencies generated by the switches are avoided. The noise elimination processing is made through the principle of digital correlated double sampling, which is equivalent to a time shifted subtraction for the sampled voltage. The low frequency 1/f noise spectrum density of the data acquisition system is reduced to be flat down to the measurement frequency lower limit, which is about 0.0001 Hz in this paper. The noise spectrum density is eliminated by more than 60 dB at 0.0001 Hz, with a residual noise floor of (9 ± 2) nV/Hz(1/2) which is limited by the intrinsic white noise floor of the ADC above its corner frequency.

We review the G measurements with time-of-swing method at HUST. Two independent experiments have been completed and an improved experiment is in progress. The first G value was determined as 6.6699(7)×10 −11 m 3 kg −1 s −2 with a relative standard uncertainty ( u r ) of 105 ppm by using a long period torsion pendulum and two cylindrical source masses. Later, this result was corrected to be 6.6723(9)×10 −11 m 3 kg −1 s −2 with u r =130 ppm after considering the density distribution of the cylinders and the air buoyancy, which was 360 ppm larger than the previous value. In 2009, a new experiment by using a simple block pendulum and spherical source masses with more homogeneous density was carried out. A series of improvements were performed, and the G value was determined to be 6.67349(18)×10 −11 m 3 kg −1 s −2 with u r =26 ppm. To reduce the anelasticity of the torsion fibre, fused silica fibres with Q 's of approximately 5×10 4 are used to measure G in the ongoing experiment. These fibres are coated with thin layers of germanium and bismuth in turn to reduce the electrostatic effect. Some other improvements include the gravity compensation, reduction of the coating layer effect, etc. The prospective uncertainty of the next G value is 20 ppm or lower.

The Weak Equivalence Principle (WEP) together with Local Position Invariance (LPI) and Local Lorentz Invariance (LLI) forms the Einstein Equivalence Principle (EEP), which is one of the basic assumptions of Einsteins General Relativity. However, most of the theories trying to unify the gravitation with the quantum world, which is mostly described by the Standard Model, indicate some violation of the WEP. So the discovery of violation of the WEP would have a very important scientific significance. Testing the WEP with the highest possible precision is always a frontier issue in the world. This paper introduces almost all the ways of testing the WEP all over the world, including using the simple pendulum, torsion balance, free fall and lunar laser ranging. Whats more, a lot of space missions have been proposed to test the WEP with a higher precision by many groups and institutions. The latest progress of these tests will also be described here.

The ongoing precision measurement of the gravitational constant G at our group is performed by using two different kinds of methods: time-of-swing method (ToS) and angular acceleration feedback method. In the two methods, the stainless steel spheres are employed as source masses, and the position stability of the spheres is an important parameter, which make suitable mounts for supporting the spheres needed extremely. In this paper, an upgraded three-point mount is introduced and tested in detail. Experimental results show that, for the sphere supported by the three-point mount used in the ToS method, the repeatability, the temperature influence, and the vibration influence are all less than 0.1 μm (about 2 ppm for the value of G). For the sphere supported by the three-point mount used in the AAF method, similar results are obtained, the largest change of the sphere's position is about 0.6 μm, introduced by a temperature change of 1 °C, which also results in an uncertainty of 2 ppm for the value of G.

This paper reports the performance of a torsion-type thrust stand suitable for studies of micro-Newton thrusters, which is developed for ground testing the micro-Newton thruster in Chinese Test of the Equivalence Principle with Optical readout space mission. By virtue of specially suspending design and precise assembly of torsion balance configuration, the thrust stand with load capacity up to several kilograms is able to measure the impulse bit up to 1350 μNs with a resolution of 0.47 μNs, and the average thrust up to 264 μN with a resolution of 0.09 μN in both open and close loop operation. A pulsed plasma thruster, the preliminary prototype developed for Chinese TEPO space mission, is tested by the thrust stand, and the results reveal that the average impulse bit per pulse is measured to be 58.4 μNs with a repeatability of about 5%.

We report a new test of the gravitational inverse square law at millimeter ranges by using a dual-modulation torsion pendulum. An I-shaped symmetric pendulum and I-shaped symmetric attractors were adopted to realize a null experimental design. The non-Newtonian force between two macroscopic tungsten plates is measured at separations ranging down to 0.4 mm, and the validity of the null experimental design was checked by non-null Newtonian gravity measurements. We find no deviations from the Newtonian inverse square law with 95% confidence level, and this work establishes the most stringent constraints on non-Newtonian interaction in the ranges from 0.7 to 5.0 mm, and a factor of 8 improvement is achieved at the length scale of several millimeters.

A new determination of the Newtonian gravitational constant $G$ is presented by using a torsion pendulum with the time-of-swing method. Compared with our previous measurement with the same method, several improvements greatly reduced the uncertainties as follows: (i) two stainless steel spheres with more homogeneous density are used as the source masses instead of the cylinders used in the previous experiment, and the offset of the mass center from the geometric center is measured and found to be much smaller than that of the cylinders; (ii) a rectangular glass block is used as the main body of the pendulum, which has fewer vibration modes and hence improves the stability of the period and reduces the uncertainty of the moment of inertia; (iii) both the pendulum and source masses are placed in the same vacuum chamber to reduce the error of measuring the relative positions; (iv) changing the configurations between the ``near'' and ``far'' positions is remotely operated by using a stepper motor to lower the environmental disturbances; and (v) the anelastic effect of the torsion fiber is first measured directly by using two disk pendulums with the help of a high-$Q$ quartz fiber. We have performed two independent $G$ measurements, and the two $G$ values differ by only 9 ppm. The combined value of $G$ is $(6.673\text{ }49\ifmmode\pm\else\textpm\fi{}0.000\text{ }18)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }{\mathrm{m}}^{3}\text{ }{\mathrm{kg}}^{\ensuremath{-}1}\text{ }{\mathrm{s}}^{\ensuremath{-}2}$ with a relative uncertainty of 26 ppm.