Physical Explanation on Designing Three Axes as Different Resolution Indexes from GRACE Satellite-Borne Accelerometer

The GRACE Earth＇s gravitational field complete up to degree and order 120 is recovered based on the same and different three-axis resolution indexes from satellite-borne accelerometer using the improved energy conservation principle. The results show that designing XA1（2） as low-sensitivity axis （3 × 10^-9 m/s^2） of accelerometer and designing YA1（2） and ZA1（2） as high-sensitivity axes （3 × 10^-10 m/s^2） are reasonable. The physical reason why the resolution of XA1（2） is one order of magnitude lower than YA1（2） and ZA1（2） is that non-conservative forces acting on GRACE satellites are mainly decomposed into YA1（2） and ZA1（2） in the orbital plane. Since XA1（2） is not orthogonal accurately to orbital plane during the development of accelerometer, the measurement of XA1（2） can not be thrown off entirely, but be reduced properly.     

Shape and gravitational field of the ellipsoidal satellites

The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite’s geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.     

Doppler characterization of laser inter-satellite links for optical LEO satellite constellations

Because of ensuring very low propagation delay between satellites, and providing global space-based broadband network services, low earth orbit (LEO) satellite constellations with laser inter-satellite links (ISLs) are considered to be the enabling technology to satisfy the increasing data traffic demand. However, significant Doppler can be observed by the onboard terminals on the ISLs, due to the high relative speed of the two communicating LEO satellites. This paper describes an analytic derivation of the Doppler wavelength shift measured by the terminal onboard a satellite on the signal transmitted through the ISLs. The Point-Ahead Mechanism of the optical ISLs is considered in the analytical expression of the Doppler wavelength shift. Then, in terms of the ISLs characteristics of the satellite constellations, the expression of Doppler wavelength shift is deduced into two aspects. First, for the full time accessing ISLs, it evolves as a function of the constellation parameters. Thus, the Doppler characterization for two kinds of interorbit full time accessing ISLs of LEO satellite constellations is analyzed. Second, for the intermittent accessing ISLs, the expression of Doppler wavelength shift is given as a function of the minimum ISL distance between two communicating satellites. And the visibility duration of the destination satellite at the source satellite is estimated for the intermittent ISLs. This work is helpful to evaluate the design of constellation networking.     

The solutions of navigation observation equations for CAPS

Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is different from the GPS broadcasting satellite navigation class, where the propagation epoch of original navigation signals for pseudo-range measurement is from a ground master control station rather than from satellite transponders. This paper addresses the establishment of the three observation equation models for the navigation and positioning system based on communications satellites, and expresses them identically to operator equations and optimized models. Furthermore, both algorithms of the linear solution for the observable characteristic equation and the least-squares solution for the condition number more than 4 are discussed, with several methods for the exact solution, such as improving the behavior of coefficient matrices, right estimation for the weighted right hand side and selection of iteration forms of solutions, and the influence of the condition number on improving navigation and positioning accuracy is also analyzed carefully. Hopefully, all the works would be contributive to further development of the navigation and positioning system based on communications satellites, and be potentially valuable to other satellite navigation and positioning systems. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815500)     

SIS accuracy and service performance of the BDS-3 basic system

On December 27,2018,the basic system of the third-generation BeiDou navigation satellite system(BDS-3)completed the deployment of its constellation of 18 MEO networking satellites as well as the construction of the operation control system(OCS)and began to provide basic navigation services to users worldwide.Compared with BDS-2,BDS-3 aims to offer users better navigation signals and higher precision with a series of new technologies.For example,the spaceborne atomic clock of BDS-3 is upgraded for higher performance,the Ka-band inter-satellite link is adopted for inter-satellite ranging and communication,and new B1C and B2a signals are broadcast in addition to B1I and B3I signals(compatible with BDS-2).In addition,a 9-parameter model based on a spherical harmonic function is employed for ionospheric delay corrections.Using the observation data from 18 satellites of the basic system,this paper conducts a comprehensive evaluation of the pseudorange measurement characteristics,signal-in-space(SIS)accuracy of navigation messages and global service capability of BDS-3.The results indicate that the pseudorange measurement multipath effect and observation noise of BDS-3 satellites are better than those of BDS-2;additionally,with the support of inter-satellite links,the user range error(URE)of the BDS-3 satellite broadcast ephemeris is better than 10 cm,the precision of the broadcast clock parameter is better than 1.5 ns,and the SIS accuracy is better than 0.6 m overall.Different from the traditional Klobuchar model,the BeiDou global broadcast ionospheric delay correction model(BDGIM)can provide ionospheric delay corrections better than 70%for worldwide single-frequency users.The service capability evaluation of the basic system consists mainly of the accuracy improvement of the B1I and B3I signals according to BDS-2 as well as the global positioning accuracy of the new signals.These results prove that the BDS-3 basic system has achieved the design goal;that is,both the horizontal and the vertical global positioning accuracies are better than 10 m(95%).In the future,6 MEO satellites as well as 3 GEO satellites and 3 IGSO satellites for regional enhancement purposes will be deployed for full operation;consequently,BDS-3 will definitely provide a higher SIS accuracy and better service capability.     

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth’s gravitational field measured from the gravity field and steady-state ocean circulation explorer(GOCE),up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry(SGG) are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth’s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth’s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.     

On a New Observable for Measuring the Lense–Thirring Effect with Satellite Laser Ranging

For a pair of twin Earth orbiting artificial satellites placed in identical orbits with supplementary inclinations, in addition to the sum of the residuals of the nodal rates, already proposed for the LAGEOS–LARES mission, also the difference of the residuals of the perigee rates could be employed, in principle, for measuring the general relativistic Lense–Thirring effect. Indeed, on one hand, the gravitomagnetic secular precessions of the perigees of two supplementary satellites in identical orbits are equal and opposite, and, on the other, the classical secular precessions induced by the multipolar expansion of the terrestrial gravitational field are equal, so that their aliasing effect cancels out in the difference of the perigees' rates. If the eccentricities of the two satellites would be chosen to be equal, contrary to the LAGEOS–LARES project, such cancellation would occur at a very accurate level. Among the time–dependent perturbations, the proposed observable would allow to cancel out the even and odd zonal gravitational tidal perturbations and some non–gravitational perturbations. With a proper choice of the inclination of the two satellites, the periods of all the uncancelled time–dependent perturbations could be made short enough to allow to fit and remove them from the signal over observational time spans of a few years. The linear perturbation induced by the terrestrial Yarkovski–Rubincam effect would affect the proposed measurement at a level well below 10^–3.     

Ocean heat content and Earth's radiation imbalance

Earth's radiation imbalance is determined from ocean heat content data and compared with results of direct measurements. Distinct time intervals of alternating positive and negative values are found: 1960-mid-1970s (−0.15), mid-1970s-2000 (+0.15), 2001-present (−0.2 W/m²), and are consistent with prior reports. These climate shifts limit climate predictability.     

低轨四星时差定位技术研究

文章重点分析影响低轨四星时差定位系统精度的主要因素;首先,从四星时差定位的基本原理出发,对四星时差定位的模型和几何精度因子进行了详细的推导,并通过仿真分析了四星构型、时差测量精度、卫星位置误差、基线长度、星座投影面积等对四星时差定位系统精度的影响;通过比较可知,在相同参数条件下,采用Y形构形,减小时差测量误差、提高卫星定位精度、增加基线长度,增大星座投影面积均等均能够提高该系统的定位精度;在低轨四星定位系统应用场景中,四星构型、卫星绝对位置测量精度、基线长度以及星座投影面积对四星时差定位系统精度影响较大,时差测量精度和卫星相对位置测量精度对四星时差定位系统精度影响较小;而在实际任务中应权衡各因素的效费比,来保证定位精度。     

Identification of Radial Distance of Plasma Dispersionless Injection Boundary from the Injection Source

Measurements of energetic particles obtained by the two geosynchronous satellites （1991-080 and LANL-97A） are performed to investigate the plasma injection boundary and source region during the magnetospheric substorms. The measurement method is developed to allow remote sensing of the plasma injection time and the radial distance of injection boundaries by using measured energy dispersion and modelling particle drifts within the Volland-Stern electric field and the dipole magnetic field model. The radial distance of the injection boundary deduced from a dispersion event observed by the LANL-97A satellite on 14 June 1998 is 7.1RE, and the injection time agrees well with the substorm onset time identified by the Polar Ultraviolet Imager. The method has been applied to an event happened at 22.9 UT on 11 March 1998, when both the satellites （1991-080 and LANL-97A） observed the dispersionless character. The results indicate that the radial distance of injection source locates at 8.1RE at magnetotail, and particles move earthward from magnetotail into inner magnetosphere at 22.5 UT.     

利用GOCE卫星数据确定全球重力场模型

利用GOCE卫星观测数据确定全球静态重力场是当前大地测量学的研究热点.本文联合2011-02-28至2012-03-05共12个月的GOCE卫星轨道和梯度数据采用直接法恢复了210阶次的重力场模型SWJTUGO01S,利用零相位的有限脉冲带通数字滤波器对GOCE梯度数据进行滤波处理,直接在梯度仪坐标系中建立梯度观测方程,避免了坐标转换过程中高精度梯度观测分量精度的损失;采用短弧积分法处理轨道数据,并利用方差分量估计确定联合解的最优权,Kuala正则化方法用于处理数据极空白问题.基于EGM2008模型和北美地区的GPS水准观测数据,对SWJTU-GO01S模型进行内外符合精度分析,结果表明:SWJTU-GO01S模型在210阶次的大地水准面误差和累计误差分别为2.1 cm和13.7 cm,整体上优于欧空局公布的第二代时域法和空域法模型的精度,在150阶以后优于ITG-GRACE2010S的精度;本文的研究为进一步联合多类卫星观测数据恢复重力场模型提供参考.     

Limitations of atom interferometry for gravitational wave observations in space

A paper published recently (Hogan et al. in Gen. Relativ. Gravit. 43:1953–2009, 2011) suggests the use of atom interferometry between satellites in Earth orbit to observe gravitational waves. The proposed altitude and satellite separation are about 1,000 and 30 km respectively. The difference in acceleration between clouds of ultracold atoms in atom interferometers near the two satellites would be detected by using laser beams between the interferometers. Because of the measurement path being very short compared with the million km or longer measurement path for a proposed laser interferometer gravitational wave antenna in space, the sensitivity to differential fluctuations in the laser phase as seen by the atoms in the two atom interferometers is very high. Problems introduced by this high sensitivity to spurious laser beam phase changes will be described in the first part of this paper. Then other limitations on the performance and on the suggested types of sources that could be observed will be discussed.     

双星光学观测体系的目标定位误差分析

为提高双星光学观测体系的定位精度,构建了新型双星光学定位系统。通过对卫星、光电观测平台的建模,构建了地惯系下平台与目标间的观测矢量模型。利用几何定位算法,推导出了地惯系下的目标定位模型与定位误差模型,并利用蒙特卡罗法获得了定位误差分布。在此基础上,引入了小波理论进行误差的优化重构,以提高双星光学观测体系的定位精度。利用测量数据进行仿真,结果表明,引入小波理论对目标定位误差进行降噪重构后,可以使目标定位精度提高30%,为工程上减小目标定位误差提供了新的思路。     

Measuring the gravitational acceleration of antimatter with an antihydrogen interferometer

The gravitational force on antimatter has never been directly measured. A method is suggested for making this measurement by directing a low-energy beam of neutral antihydrogen atoms through a transmission-grating interferometer and measuring the gravitationally-induced phase shift in the interference pattern. A 1% measurement of the acceleration due to the Earth's gravitational field (¯ g) should be possible from a beam of about 10⁵ or 10⁶ atoms. If more antihydrogen can be made, a much more precise measurement of¯ g would be possible. A method is suggested for producing an antihydrogen beam appropriate for this experiment.     

Satellite orbits and their geophysical implications

Small changes in the orbits of satellites near to the earth have revealed new information about the earth's gravitational field and atmosphere. This article explains the main properties of satellite orbits and describes the discoveries which have been made with their help in the following branches of geophysics: the figure of the earth and the gravitational field; the density of the upper atmosphere and its variations, which have proved to be linked with solar activity; and, finally, other properties of the atmosphere, such as temperature and winds.     

高精度千赫兹流动激光测距系统中国西部地区实测结果分析

为了解决人造卫星激光测距观测站在我国东西部地区分布不均衡的现状,中国地震局地震研究所采用方便运输的载车结构和皮秒级千赫兹半导体激光器,结合自行研制的皮秒级事件计数器和纳秒级距离门,研制了新一代的大口径流动卫星激光测距系统TROS1000.TROS1000具备千赫兹流动激光测距的能力,并且具有机动灵活、架设周期短等特点.2019年9月,TROS1000抵达中国科学院新疆天文台南山观测站,在我国西部地区首次获取千赫兹激光观测数据.经过数据预处理,中低轨卫星的单次精度优于14 mm,高轨卫星的单次精度优于19 mm,与上一代流动激光测距系统相比,其单次精度更高,有效回波信号更多,目标探测能力更强.     

Fundamental physics with the ESA mission GAIA

esa advisory committees have selected the astrometry mission gaia as one of the future cornerstones of the science program. gaia is primarily a mission to study the history, formation and evolution of the Galaxy from astrometric, photometric and spectroscopic measurements, but it also displays remarkable capabilities in some areas of fundamental physics. After introducing briefly the measurement principles and the expected accuracy, I focus on the three topics most relevant for the physicists: the definition and realization of a quasi-inertial machian frame, the testing of the PPN formulation of the gravitational theory and finally a determination of the possible time change of the gravitational constant.     

Limitations to testing the equivalence principle with satellite laser ranging

We consider the possibility of testing the equivalence principle (EP) in the gravitational field of the Earth from the orbits of LAGEOS and LAGEOS II satellites, which are very accurately tracked from ground by laser ranging. The orbital elements that are affected by an EP violation and can be used to measure the corresponding dimensionless parameter η are semimajor axis and argument of pericenter. We show that the best result is obtained from the semimajor axis, and it is limited—with all available ranging data to LAGEOS and LAGEOS II—to η ≃ 2 × 10⁻⁹, more than 3 orders of magnitude worse than experimental results provided by torsion balances. The experiment is limited because of the non uniformity of the gravitational field of the Earth and the error in the measurement of semimajor axis, precisely in the same way as they limit the measurement of the product GM of the Earth. A better use of the pericenter of LAGEOS II can be made if the data are analyzed searching for a new Yukawa-like interaction with a distance scale of one Earth radius. It is found that the pericenter of LAGEOS II is 3 orders of magnitude more sensitive to a composition dependent new interaction with this particular scale than it is to a composition dependent effect expressed by the η parameter only. Nevertheless, the result is still a factor 500 worse than EP tests with torsion balances in the gravitational field of the Earth (i.e. at comparable distance), though a detailed data analysis has yet to be performed. While EP tests with satellite laser ranging are not competitive, laser ranging to the Moon has been able to provide a test of the EP almost 1 order of magnitude better than torsion balances. We show that this is due to the much greater distance of the test masses (the Earth and the Moon) from the primary body (the Sun) and the correspondingly smaller gradients of its gravity field. We therefore consider a similar new experiment involving the orbit of LAGEOS: testing LAGEOS and the Earth for an EP violation in the gravitational field of the Sun. We show that this test may be of interest, though it is a factor 300 less sensitive than in the case of the Moon due to the fact that LAGEOS is closer to the Earth than the Moon and consequently its orbit is less affected by the Sun. The limitations we have pointed out for laser ranging can be overcome by flying in low Earth orbit a spacecraft carrying concentric test masses of different composition with the capability, already demonstrated in ground laboratories, to accurately sense in situ any differential effects between them. An erratum to this article can be found at     

On the vortex formation at the moving front of lightweight granular particles

The formation of vortices at a moving front of lightweight granular particles is investigated experimentally. The particles used in this study are made of polystyrene foam with three different diameters of nearly uniform size. Pairs of vortices are found to emerge at the moving front at regular intervals, thereby forming a wavy pattern. Once the vortices are produced, the flow velocity tends to increase. A simple analysis suggests the existence of a velocity boundary layer at the moving front, whose thickness increases with increasing particle diameter. The frontal radius of each vortex pair is about the size of this boundary layer; when the radius exceeds this size, the front tends to bifurcate into a train of vortices with the size of the boundary layer. The formation of twin vortices leads to a reduction in the air drag force exerted on the system, and thereby the system attains a higher flow velocity, i.e., a higher conversion rate of gravitational potential energy to the kinetic energy of the particle motion. The higher conversion rate of potential energy thus feeds back to the development of the vortex motion, resulting in the twin vortex formation.     

A new method for determination of satellite orbits by transfer

The original idea of a new method for determination of satellite orbits by transfer is from Two-Way Satellite Time and Frequency Transfer (TWSTFT). The original method is called “determination of satellite orbit by transfer”. The method is not only for determination of satellite orbit but also for the time transfer with high accuracy and precision. The advantage is that the accuracy and the precision for determination of satellite orbit are very high and the new method is favorable for various applications. The combination of various signals disseminated and received forms various modes of satellite orbit determinations. If receivers at stations receive the own station-disseminated signals via a satellite transponder, it forms an orbit determination mode called “receiving the own station-disseminated signals mode”. If receivers at all stations receive the signals disseminated from the master station via satellite transponders, it forms an orbit determination mode called “receiving the master station-disseminated signals mode”. If all of receivers at stations receive all stations-disseminated signals via satellite transponders, it forms an orbit determination mode called “receiving all stations-disseminated signals mode”. Also there are other combinations of signals for satellite orbit determination. For different orbit determination modes with different signal combinations, their rigorous formulae of processing are hereby presented in this paper. The accurate and the precise satellite orbit determination for both of the modes, “receiving the own station-disseminated signals mode” and “receiving the master station-disseminated signals mode” is attempted. It shows that the accuracy and precision for both of modes are nearly the same, the ranging accuracy is better than 1 cm, and the observation residuals of satellite orbit determination are better than 9 cm in the observation duration of 1 day. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815503100453001)