V. K. Milyukov

TianQin: a space-borne gravitational wave detector

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiments error budget and discuss the projects overall feasibility. Given the current level of technology readiness, we expect TianQin to be flown in the second half of the next decade.

Methodology and instrumentation for testing the weak equivalence principle in stratospheric free fall

The use of the GiZero free-fall facility for testing the weak equivalence principle is discussed in this article. GiZero consists of a vacuum capsule, released from a balloon at an altitude of 40 km, which shields an experimental apparatus free falling inside the capsule itself. The expected residual acceleration external to the detector is 10−12 g (with g the Earth’s gravitational acceleration) for the 30 s free fall. A common-mode rejection factor of about 10−4 reduces the residual noise differential output to only 10−16 g. The gravity detector is a differential accelerometer with two test masses with coincident center of masses (i.e., zero baseline) with capacitive pick ups. Preparatory experiments have been conducted in the laboratory with a precursor detector by measuring controlled gravity signals, at low frequency, and by observing the Luni-Solar tides. The estimated accuracy in testing the weak equivalence principle, with a 95% confidence level, is 5×10−15 in a 30 s free fall. When compared to orb...

Deformation Processes in the Lithosphere Related to the Nonuniformity of the Earth's Rotation

The series of observations conducted at the Baksan and Protvino deformation stations in the Northern Caucasus and the Central Russian Plain, respectively, and the length-of-day (LOD) data describing the variable rate of the Earth’s rotation are used to study the relation between the deformation processes in the lithosphere and the global geodynamics of the Earth over short time intervals. The methods applied are based on high-resolution spectral analysis, analysis of the coherence of the studied processes, and correlation analysis. A significant (95%) correlation is revealed between the local deformation fields at two remote observation stations, which proves the existence of a global component in the Earth’s deformation field that manifests itself at characteristic time intervals of up to 3–4 weeks. At the same level of significance, the correlation between the local deformation fields and variations in the rate of the Earth’s rotation has also been identified. It is shown that the found correlations in the tidal low-frequency range are caused by the direct impact of the long-period tidal loading (Mf and Mtm waves) on the lithosphere and the length-of-the-day (LOD). The global mechanisms giving rise to the correlation of these processes in the nontidal range require further study.

Measurement of Density Inhomogeneity for Glass Pendulum

The density inhomogeneity of a glass pendulum is determined by an optical interference method. The relative variations of the densities over a volume with sizes of 5 × 5 × 5 mm3 are (0.64 ± 0.97) × 10−5 and (0.99 ± 0.92) × 10−5 for the K9 glass and silica glass pendulum, respectively. These variations of densities contributing to the relative uncertainties of the Newtonian gravitational constant G are 0.20 ppm and 0.21 ppm in our experiment on measurement of G.

Observations of crustal tide strains in the Elbrus area

Results of observations of tidal strains of the crust in the tectonically active Elbrus area of the Northern Caucasus carried out with the use of the Baksan SSAI laser interferometer strainmeter over the period from 2003 through 2006 are presented. Harmonic analysis is performed with the help of the ETERNA software package. Statistically significant time variations in the amplitudes of the main tidal waves M2 and O1 are revealed. The influence of the topography on tidal strains in the Baksan gorge is estimated at 22% (an increase in the measured strain values). The reduced amplitude factors of the main diurnal (O1) and semidiurnal (M2) waves are underestimated. Numerical modeling of tidal anomalies produced by regional heterogeneous inclusions is performed in a 2-D approximation. The observed anomaly of the M2 wave (12%) is shown to be due to the influence of the main magma-controlling fault associated with the deep magma source of the Elbrus dormant volcano.

The free oscillations of the earth excited by three strongest earthquakes of the past decade according to deformation observations

Based on the deformation data provided by the Baksan laser interferometer-strainmeter measurements, the free oscillations of the Earth (FOE) excited by the three strongest earthquakes of the past decade are analyzed. These seismic events include the Great Sumatra-Andaman earthquake that occurred in 2004 in the Indian Ocean, the Mauli earthquake of 2010 in Chile, and the Great Tohoku earthquake of March 2011 in Japan. The frequency-time structure of the free oscillations is studied, and the pattern of interaction between the modes with close frequencies (cross-coupling effect) is explored. For each earthquake, the correspondence of the observed FOE modes to the model predictions by the PREM model is investigated. A reliable consistent shift towards the high frequency of the toroidal modes with angular degree l = 12–19 is revealed. The maximal energy density of the toroidal oscillations is concentrated in the upper mantle of the Earth. Therefore, the established effect corresponds to the higher velocity of the shear waves in the upper mantle than it is predicted by the PREM model.

Preliminary determination of Newtonian gravitational constant with angular acceleration feedback method

This paper describes the preliminary measurement of the Newtonian gravitational constant G with the angular acceleration feedback method at HUST. The apparatus has been built, and preliminary measurement performed, to test all aspects of the experimental design, particularly the feedback function, which was recently discussed in detail by Quan et al. The experimental results show that the residual twist angle of the torsion pendulum at the signal frequency introduces 0.4 ppm to the value of G. The relative uncertainty of the angular acceleration of the turntable is approximately 100 ppm, which is mainly limited by the stability of the apparatus. Therefore, the experiment has been modified with three features: (i) the height of the apparatus is reduced almost by half, (ii) the aluminium shelves were replaced with shelves made from ultra-low expansion material and (iii) a perfect compensation of the laboratory-fixed gravitational background will be carried out. With these improvements, the angular acceleration is expected to be determined with an uncertainty of better than 10 ppm, and a reliable value of G with 20 ppm or below will be obtained in the near future.

The Newtonian gravitational constant: Modern status of measurement and the new CODATA value

Measurements of G, the Newtonian constant of gravitation, in laboratory experiments have a more than two hundred years’ history. Although the accuracy of the best modern experimental measurements of G reaches 15–40 ppm, the scatter of the measured values is large enough, and the knowledge of the absolute value of G is still rather poor. The results of the G measurements which were used for CODATA adjustments, as well as the CODATA values, are reviewed in the paper.

Velocities of contemporary movements of the Northern Caucasus estimated from GPS observations

The velocity field of the Northern Caucasus based on the results of observations at the Northern Caucasus Geodetic Network (NCGN) stations is represented in the paper. Appreciable horizontal displacement to the northeast with velocity of 26–28 mm/yr relative to the International Terrestrial Reference Frame (ITRF2008) is established. General shortening of the region at a rate of 1–2 mm/yr relative to fixed Eurasia is a source of the contemporary geological and seismic activity in the boundary zone between the Caucasus and the East European Platform.

G measurements with time-of-swing method at HUST

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 m3 kg−1 s−2 with a relative standard uncertainty (ur) 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 m3 kg−1 s−2 with ur=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 m3 kg−1 s−2 with ur=26 ppm. To reduce the anelasticity of the torsion fibre, fused silica fibres with Qs of approximately 5×104 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.