A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

Gravity gradient distribution in China's Mainland from GOCE satellite gravity gradiometry data

At present, gravity field and steady-state ocean circulation explorer（GOCE） gravity data are always used to compute regional gravity anomaly and geoid height. In this study, the latest GOCE gravity field model data（from Oct. 2009 to Jul. 2010） are used to compute the gravity gradient of China's Mainland according to a rigorous recursion formula（in all the six directions）. The results show that the numerical values of the gravity gradients are larger in the T rr direction than those in the other directions. They reflect the terrain characteristics in detail and correlate with the regional tectonics; however, in the T ql and T r l directions,the numerical values are relatively smaller and the gravity gradients in the T r l direction do not reflect the terrain characteristics in detail.

Modeling of Earth’s Gravity Fields Visualization Based on Quad Tree

The problems of the earth's gravity fields' visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth's gravity fields' data is discussed in the paper by using LOD algorithm based on Quad Tree. First, this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids' rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth's gravity fields.

Chinese Gravimetry Augment and Mass Change Exploring Mission Status and Future

The satellite gravimetry technology effectively recovers the global Earth’s gravity field.Since 2000s,HL-SST satellite CHAMP,LL-SST satellite GRACE,Gravity Gradient Measurement(GGM)satellite GOCE have been launched successfully,producing some Earth’s gravity models solely from satellites data.However,the space and time resolution of the Earth’s gravity fields do not adequately satisfy scientific objectives.The main reason is that the gravimetry satellites are not enough and observation data insufficient.The paper outlines the current and future status of Chinese gravity satellite missions.The Chinese gravimetry satellite system,named Chinese Gravimetry augment and Mass change exploring mission(ChiGaM),successfully launched in Dec.2021 after four years of production and over a year of calibration and valiation.The accelerometer,K-band ranging system and the three stellar sensors,among others,were precisely calibrated and trimmed.The satellite mass center was determined and coordinated with the proof center of accelerometer with an accuracy 100μm.The inter-satellite ranging system and BDS/GPS receiver operate together seamlessly.The range and range rate noise is less than 3μm/Hz^(1/2) and 1μm/s/Hz^(1/2),respectively,in band of 0.025~0.1 Hz.The electrostatic suspension accelerometer is working well.Its high-sensitive axis noise level is 3×10^(-10) m/s^(2)/Hz^(1/2)near the frequency 0.1 Hz,and 1×10^(-9) m/s^(2)/Hz^(1/2) for the less-sensitive axis.Meanwhile the BDS/GPS receiver is used to achieve data for precise orbit determination,yielding an orbit result with accuracy better than 2 cm.When compared with KBR observations,the RMS of the bias is less than 1 mm.Besides above mission,next gravimetric satellite is being developed now.TQ-2 mission is designed as a totally experimental satellite for gravitational wave detection at low Earth orbit,which can detect the Earth’s gravity field simultaneously.The Bender-type mission is considered the most promising configuration for TQ-2 and consists of two polar satellites and two inclined satellites.Due to the extra observations at the east-west direction derived from the inclined satellite pair,significant improvements has been made in detecting temporal signals with higher accuracy and spatial-temporal resolution.To achieve the scientific goal,the ACC MBW can shift from 0.001~0.1 Hz to 0.004~0.1 Hz for ACC,and the LRI MBW can shift from 0.01~1 Hz to 0.1~1 Hz.For future research,a gravimetric potential survey using cold-atomic-clock based on the general relativity theory,cold atom gradiometer should be pursued.Gravimetric technologies should be mined and researched,and the gravimetry satellite constellation should be developed,so as to improve the time resolution and space resolution for meeting the requirements of geophysics,geodesy,earthquake,water resources environment,oceanography,etc.

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

Establishment and Analysis of the Spectral Relationship Between Range-Rate and Gravity Potential Based on Energy Conservation

The spectral relationship between range-rate measurements and the gravity potential for low-low satellite-to-satellite tracking mission was established based on the energy conservation theory. Then the performances of satellite separation, the orbital altitude, and the accuracy of range-rate measurements in recovering the earth＇s gravity field were simulated and analyzed by this method. Finally, the cumulative geoid errors of the reference mode were obtained by using the configuration parameters of the GRACE mission. By comparing the cumulative geoid errors of the reference mode and GGMO2S and EIGEN-GRACEO2S models, it basically reflected the performance of GRACE and proved the feasibility of this method.