Electrostatic gravity gradiometer design for the future mission

Satellite gravity gradiometry has been applied in GOCE mission to obtain higher harmonics of the Earth’s gravity mapping. In-orbit results showed that the precision of GOCE gradiometry achieved a level of 10–20 mE/Hz^1/2 in the bandwidth of 38–100 mHz, and the major error source came from the intrinsic noise of the core sensor electrostatic accelerometer. Two schemes for improving sensitivity of such accelerometer are presented by optimizing the parameters to reduce the dynamic range and choosing the heavier proof mass to suppress the thermal noise limited by the discharging gold wire. As a result, an accelerometer with a better resolution of 6.6×$6.6\times$10⁻¹³ m/s²/Hz^1/2 could be developed, and then a precision of 3 mE/Hz^1/2, corresponding to a spatial resolution of about 78 km half wavelength, is achievable for the future satellite gradiometric mission.     

Finding the suitable drag-free acceleration noise level for future low-low satellite-to-satellite tracking geodesy missions

This paper evaluates the impact of residual acceleration noise on the estimation of the Earth’s time-varying gravity field for future low-low satellite-to-satellite tracking missions. The goal is to determine the maximum level of residual acceleration noise that does not adversely affect the estimation error. The Gravity Recovery And Climate Experiment (GRACE) has provided monthly average gravity field solutions in spherical harmonic coefficients for more than a decade. It provides information about land and ocean mass variations with a spatial resolution of ～350?km and with an accuracy within 2?cm throughout the entire Earth. GRACE Follow-on was launched in May 2018 to advance the work of GRACE and to test a new laser ranging interferometer, which measures the range between the two satellites with higher precision than the K-Band ranging system used in GRACE. Moreover, there have been simulation studies that show, an additional pair of satellites in an inclined orbit increases the sampling frequency and reduces temporal aliasing errors. Given the fact that future missions will likely continue to use the low-low satellite-to-satellite tracking formation with laser ranging interferometry, it is expected that the residual acceleration noise will become one of the largest error contributor for the time-variable gravity field solution. We evaluate three different levels of residual acceleration noise based on demonstrated drag-free systems to find a suitable drag-free performance target for upcoming geodesy missions. We analyze both a single collinear polar pair and the optimal double collinear pair of drag-free satellites and assume the use of a laser ranging interferometer. A partitioned best linear unbiased estimator that was developed, incorporating several novel features from the ground up is used to compute the solutions in terms of spherical harmonics. It was found that the suitable residual acceleration noise level is around 2?×?10^?12?ms^?2?Hz^?1/2. Decreasing the acceleration noise below this level did not result in more accurate gravity field solutions for the chosen mission architecture.     

Magnetic torquer induced disturbing signals within GRACE accelerometer data

The GRACE (Gravity Recovery And Climate Experiment) gravity field satellite mission was launched in 2002. Although many investigations have been carried out, not all disturbances and perturbations upon satellite instruments and sensors are resolved yet. In this work the issue of acceleration disturbances onboard of GRACE due to magnetic torquers is investigated and discussed. Each of the GRACE satellites is equipped with a three-axes capacitive accelerometer to measure non-gravitational forces acting on the spacecraft. We used 10 Hz Level 1a raw accelerometer data in order to determine the impact of electric current changes on the accelerometer. After reducing signals which are induced by highly dominating processes in the low frequency range, such as thermospheric drag and solar radiation pressure, which can easily be done by applying a high-pass filter, disturbing signals from onboard instruments such as thruster firing events or heater switch events need to be removed from the previously filtered data. Afterwards the spikes which are induced by the torquers can be very well observed. Spikes vary in amplitude with respect to an increasing or decreasing current used for magnetic torquers, and can be as large as 20 nm/s². Furthermore, we were able to set up a model for the spikes of each scenario with which we were able to compute model spike time series. With these time series the spikes can successfully be removed from the 10 Hz raw accelerometer data. Spectral analysis of the time series reveal that an influence onto gravity field determination due to these effects is very unlikely, but can theoretically not be excluded.     

Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

The prospects of future satellite gravimetry missions to sustain a continuous and improved observation of the gravitational field have stimulated studies of new concepts of space inertial sensors with potentially improved precision and stability. This is in particular the case for cold-atom interferometry (CAI) gradiometry which is the object of this paper. The performance of a specific CAI gradiometer design is studied here in terms of quality of the recovered gravity field through a closed-loop numerical simulation of the measurement and processing workflow. First we show that mapping the time-variable field on a monthly basis would require a noise level below $5\text{mE}/\sqrt{\text{Hz}}$. The mission scenarios are therefore focused on the static field, like GOCE. Second, the stringent requirement on the angular velocity of a one-arm gradiometer, which must not exceed ${10}^{-6}$?rad/s, leads to two possible modes of operation of the CAI gradiometer: the nadir and the quasi-inertial mode. In the nadir mode, which corresponds to the usual Earth-pointing satellite attitude, only the gradient $V_{\mathit{yy}}$, along the cross-track direction, is measured. In the quasi-inertial mode, the satellite attitude is approximately constant in the inertial reference frame and the 3 diagonal gradients $V_{\mathit{xx}}\text{,}{V}_{\mathit{yy}}$ and $V_{\mathit{zz}}$ are measured. Both modes are successively simulated for a 239?km altitude orbit and the error on the recovered gravity models eventually compared to GOCE solutions. We conclude that for the specific CAI gradiometer design assumed in this paper, only the quasi-inertial mode scenario would be able to significantly outperform GOCE results at the cost of technically challenging requirements on the orbit and attitude control.     

General Relativity Accuracy Test (GReAT): New configuration for the differential accelerometer

We presents the results of an activity concerning the test of the Einstein Weak Equivalence Principle with an accuracy of about 5 × 10⁻¹⁵. The experiment will be performed in an “Einstein elevator” using a differential accelerometer with a final sensitivity of about 10⁻¹⁴ g_⊕/Hz^1/2. The differential accelerometer is spun about an horizontal axis at a frequency in the range 0.5–1 Hz in order to modulate, during the free fall, the signal from a possible violation of the Equivalence Principle. In the paper the perturbing effects with the same signature of the possible violation are analyzed and constrained. The experimental results obtained in the laboratory with a first prototype of the differential accelerometer are discussed, comparing this results with those obtained using a new prototype.     

Wave and plasma measurements on the Vega-1 and Vega-2 spacecraft in the environment of comet Halley

The Vega-1 and Vega-2 wave and plasma measurements performed on 6 and 9 March 1986 in the environment of comet Halley present similar characteristics. Field spectral intensity of up to $\text{5}\text{mVm}{}^{\mathrm{?1}}\text{Hz}{}^{\mathrm{?}}\text{1}\text{2}$ at 300 Hz is measured at closest approach; enhanced signals are detected in the whistler mode and in the vicinity of the lower hybrid resonance frequency within respective average distances of 130,000 km and 60,000 km from the nucleus. The plasma density rises from 100 cm^?3 at 200,000 km up to 3000 cm^?3 at 25,000 km. The spacecraft potential is of the order of +3 V beyond a distance of 200,000 km and decreases to about +0.5 V at 8,000 km.     

A spectroscopic measurement of high velocity spray plasma from an M-class flare and coronal mass ejection

The M1.5-class flare and associated coronal mass ejection (CME) of 16 February 2011 was observed with the Extreme ultraviolet Imaging Spectrometer on board the Hinode spacecraft. Spray plasma associated with the CME is found to exhibit a Doppler blue-shift of 850 km s^?1 – one of the largest values reported from spectroscopy of the solar disk and inner corona. The observation is unusual in that the emission line (Fe xii 193.51 Å) is not observed directly, but the Doppler shift is so large that the blue-shifted component appears in a wavelength window at 192.82 Å, intended to observe lines of O v, Fe xi and Ca xvii. The Fe xii 195.12 Å emission line is used as a proxy for the rest component of 193.51 Å. The observation highlights the risks of using narrow wavelength windows for spectrometer observations when observing highly-dynamic solar phenomena. The consequences of large Doppler shifts for ultraviolet solar spectrometers, including the upcoming Multi-slit Solar Explorer (MUSE) mission, are discussed.     

The X-ray properties of normal galaxies

An extensive program to study nearby normal galaxies was carried out by various observers using the imaging instruments on the $\text{Einstein}$ Observatory; more than 50 such galaxies were detected with 0.5 – 3.0 keV luminosities ranging from 2 × 10³⁸ ergs s^?1 to 3 × 10⁴¹ergs s^?1. The X-ray luminosity of normal galaxies is ~2 × 10^?4 of the optical luminosity and shows no strong correlation with morphological type. For the nearest galaxies, (the Large and Small Magellanic Clouds, M31 and M33,) studies, performed with the Observatory, were comparable to the $\text{Uhuru}$ survey of the Galaxy. Approximately 30 new SNR were recognized in the Magellanic Clouds as a result. Over 90 sources were detected in M31 of which at least 20 are identified with globular cluster. The numbers of luminous (>10³⁷ ergs s^?1) sources detected in the nearest galaxies per unit mass are similar to that found in our own galaxy. Individual X-ray sources in the arms of nearby spirals can be very luminous; seven with luminosities in excess of 10³⁹ergs s^?1 have been discovered. The nuclei of some, but not all, normal galaxies are luminous X-ray sources; X-ray activity is not presently predictable from the radio or optical properties of the nucleus.     

Estimation of sediment settling velocity in estuarine and coastal waters using optical remote sensing data

A robust method has been developed for estimating sediment settling velocity (w_s) from high resolution optical remote sensing data in estuarine, coastal and harbor waters. This method estimates settling velocity as a function of the drag coefficient (C_d), Reynolds number (Re), grain size (D₅₀), specific gravity (Δ_SG) and grain shape (in terms of the Corey Shape Factor – CSF). These parameters were derived from the particulate inherent optical properties such as backscattering (b_bp), beam attenuation (c_p), suspended sediment concentration and turbidity using Landsat 8 OLI and HICO data. Preliminary results for the Gulf of Cambay in the eastern Arabian Sea and Yangtze river estuary in the East China Sea, showed that satellite-retrieved settling velocities (m?s^?1) varied from very low values in clear oceanic waters, intermediate values in coastal waters, to very high values in river plumes and sediment-laden coastal waters. The remote sensing retrievals of sediment properties and their settling velocities were generally consistent with the field and laboratory results, which indicate that the proposed methodology will have important implications in various coastal engineering, environmental and management studies.     

Effect of gravity on coupled convective and interfacial instabilities during directional solidification

We investigate the role of gravity in a linear stability analysis of the onset of coupled convective and morphological instabilities during directional solidification at constant velocity of a dilute alloy of tin in lead. For solidification vertically upwards, the temperature gradient alone would cause a negative density gradient and the solute gradient alone would cause a positive density gradient. Two types of instability are found, a convective type that occurs for long wavelengths and a morphological type that occurs for short wavelengths. In general, these are coupled but the morphological instabilities are practically independent of gravity and thus correspond to the predictions of previous morphological stability theory in which density changes and convection are neglected. The convective instabilities depend strongly on gravity; for a growth velocity of V = 1 μm/s and a temperature gradient in the liquid of G_L = 200 K/cm, the critical concentrations for convective instabilities are 3.1 × 10^?4, 3.1 × 10^?2 and 2.39 wt. % for g_e = 980 cm/s², 10^?4 g_e and 10^?6 g_e, respectively. For low velocities, the convective instabilities occur at much lower solute concentrations than the morphological instabilities whereas at high velocities, the reverse is true. At intermediate velocities where the changeover takes place, there are oscillitory instabilities of mixed character whose periods range from 60 s at g_e to 6 × 10⁴ s at 10^?6 g_e.     

Transport of ions in presence of induced electric field and electrostatic turbulence: Source of ions injected into ring current

The transport of ions from the polar ionosphere to the inner magnetosphere during stormtime conditions has been computed using a Monte Carlo diffusion code. The effect of the electrostatic turbulence assumed to be present during the substorm expansion phase was simulated by a process that accelerated the ions stochastically perpendicular to the magnetic field with a diffusion coefficient proportional to the energization rate of the ions by the induced electric field. This diffusion process was continued as the ions were convected from the plasma sheet boundary layer to the double-spiral injection boundary. Inward of the injection boundary, the ions were convected adiabatically. By using as input an O⁺ flux of 2.8 × 10⁸ cm^?2 s^?1 (w > 10 eV) and an H⁺ flux of 5.5 × 10⁸ cm^?2 s^?1 (w > .63 eV), the computed distribution functions of the ions in the ring current were found to be in good agreement, over a wide range in L (4 to 8), with measurements made with the ISEE-1 satellite during a storm. This O⁺ flux and a large part of the H⁺ flux are consistent with the DE satellite measurements of the polar ionospheric outflow during disturbed times.     

Energetic particles in the night-time middle- and low-latitude ionosphere

Data are presented on the zones of energetic particle precipitation at middle and low latitudes observed during and after magnetic storm injection events. Satellite measurements of the equatorial zone ion flux (～ 10³ - 10⁴ cm^?2 s^?1 sr^?1 for E > 45 keV at 240 km) are consistent with the development of a temporary low altitude ion radiation belt at the magnetic equator. In the midlatitude ion zone the flux (～ 10³ - 10⁵ ions cm^?2 s^?1 sr^?1 for E > 45 keV at 220 km) is directly related to magnetic activity while the midlatitude electron zone flux has a delayed response (～ 4 days).     

Experiment VARIANT – first results from Wave Probe instrument

The international experiment VARIANT was carried out onboard Ukrainian remote sensing satellite SICH-1M launched 2004, December 24. In spite of other than planned satellite orbit and onboard systems failure about 11 telemetric files from VARIANT payload were obtained. Due to episodic and random payload switching the main goal of VARIANT experiment - study of field aligned currents and monitoring of electromagnetic state of the ionosphere – was not possible to realize. However the data analysis from VARIANT instrumentation allowed us to obtain for the first time a reliable confirmation of proper operation in ionospheric plasma of a new device developed for wave activity study – Wave Probe, which consists of compact combination of Split Langmuir Probe working at floating potential and search-coil magnetic field sensor. Such a probe can simultaneously measure variations of one component of spatial current density and a perpendicular component of magnetic field with a spectral sensitivity threshold up to 0.1 pA/(cm² Hz^1/2) and 0.03 pT/Hz^1/2, respectively.     

Highly variable X-ray emitting objects in the Rho Oph dark cloud

The Rho Ophiuchi dark cloud region has been the subject of an extensive guest investigation using the $\text{Einstein}$ Observatory. The set of observations comprise 14 IPC fields and 3 HRI fields. The densest part of the cloud has been observed 6 times. Forty seven sources were detected at a level > 3.5 σ and twenty more above 2 σ. The majority of these sources have optical, IR, or even radio continuum counterparts; nine are identified with known T Tauri stars, while several others are identified with stars showing H α in emission. All show a high degree of time variability; flux variations reach factors of 5 in a few hours, or 25 in a day. Apparent luminosities are in the range 10(30) – 10(31)(1) erg.s^?1. The possibility that the X-ray variability is due to flares is examined. If this interpretation is correct, one source has been the seat of the largest stellar flare ever recorded in X rays [L_x = 10(32) erg.s^?1, E_x ?10(36) ergs^-].     

Aeronomie de la haute atmosphere de Venus

Nous pre´sentons les re´sultats pre´liminaires d'un mode`le photochimique de la haute atmosphe`re de Ve´nus (60 – 200 km) en nous plac¸ant dans le cas ou`l'hydroge`ne mole´culaire est abondant ([H₂]～10 ppm). L'abondance d'hydroge`ne dans l'exosphe`re est compatible avec un coefficient de diffusion turbulente de 5 · 10⁶ cm² s^?1 et un flux d'e´chappement proche du flux limite.     

基于非线性变换的加速度计误差标定与补偿CSCD

为提高三轴加速度计测量精度,分析其误差来源和产生机理,建立了误差模型;根据误差模型和重力场幅值不变特性,推导出非线性观测方程。引入两个未知的参数向量,通过数学变换把非线性观测方程变形为关于新未知参数的线性方程;然后采用批量最小二乘法求出新的未知参数,并根据误差模型参数和新未知参数之间的关系,利用逆解析运算求出对应的零点偏差、灵敏度误差和三轴不正交误差。实验结果表明,加速度计正负误差峰值间距可以减小100倍左右,精度可达10-3m/s2,并具有很好的可重复性。该方法算法效率较高,补偿效果显著。     

Validation of the in-flight calibration procedures for the MICROSCOPE space mission

The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of 10^-15${10}^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.     

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.