强不规则天体引力场中的动力学研究进展

小行星探测与彗星探测是深空探测的重要方面。一般来说,小行星和彗星因质量都不足以使得万有引力克服应力达到流体静力学平衡,而具有强不规则的外形。研究强不规则天体引力场中的动力学行为及其内在机制,是探测器被不规则天体捕获并对其形成近距离探测轨道的基础。从引力场模型和动力学行为两个方面综述了强不规则天体引力场中动力学的研究进展,在引力场模型的研究方面介绍了强不规则天体引力场建模的球谐函数摄动展开模型、简单特殊体模型及多面体模型的研究现状,在动力学机制的研究方面介绍了强不规则天体引力场中的周期轨道和拟周期轨道、平衡点、流形、分岔与共振以及混沌运动的研究现状,指出了这些方面研究的重点与难点。分析了强不规则体引力场中动力学的研究趋势。     

Convection and impurity distribution in crystal growth in low-gravity environments

Investigations conducted earlier by the authors have established that due to the steady-state field of body forces, convection is capable of giving rise to macroinhomogeneity in transverse impurity distribution in crystals. In the case of semiconductor materials the maximal value of this inhomogeneity is due to a weak convection in the melt, typical of low-gravity conditions. However, in addition to steady gravitational convection, other factors ignored previously, may also be employed in conducting experiments in low-g environments. The present paper discusses the results of theoretical studies of some factors influencing impurity distribution in the melt and the crystal.     

基于卫星自旋的纯引力轨道万有引力干扰抑制

一个称为“内卫星”的验证质量块位于外卫星的内部空腔中,不与外卫星接触而自由飞行,由于外卫星的屏蔽,其不受大气阻力、太阳光压等干扰作用,沿着纯引力轨道飞行。外卫星会对内卫星产生万有引力作用,是内卫星纯引力轨道的主要残余干扰。根据卫星相对运动动力学方程,建立了万有引力干扰对内卫星纯引力轨道影响的分析模型;基于将外卫星绕轨道面法向旋转以调制万有引力的策略,建立了外卫星自旋对万有引力干扰影响的抑制模型。以内编队纯引力飞行系统为例,对比计算了外卫星有无自旋时万有引力干扰对内卫星纯引力轨道的影响。基于模型的分析表明,外卫星自旋能够显著抑制万有引力干扰对内卫星纯引力轨道的长期影响;实例计算表明,万有引力干扰的天长期影响能够降低5~7个数量级。     

Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field

We present an integral-based approach for high-resolution regional recovery of the gravitational field in this article. We derive rigorous remove-compute-restore integral estimators relating the line-of-sight gravitational acceleration to an arbitrary order radial derivative of the gravitational potential. The integral estimators are composed of three terms, i.e., the truncated integration, the low-frequency line-of-sight gravitational acceleration, and the high-frequency truncation error (effect of the distant zones). We test the accuracy of the integral transformations and of the integral estimators in a closed-loop simulation over the Montes Jura region on the nearside of the Moon. In this way, we determine optimal sizes of integration radii and grid discretisation. In addition, we investigate the performance of the regional integral inversion with synthetic and realistic GRAIL observations. We demonstrate that the regional inversion results of the disturbing gravitational potential and its first order radial derivative in the Montes Jura mountain range are less contaminated by high-frequency noise than the global spherical harmonic models.     

Detecting gravitational waves from accreting neutron stars

The gravitational waves emitted by neutron stars carry unique information about their structure and composition. Direct detection of these gravitational waves, however, is a formidable technical challenge. In a recent study we quantified the hurdles facing searches for gravitational waves from the known accreting neutron stars, given the level of uncertainty that exists regarding spin and orbital parameters. In this paper we reflect on our conclusions, and issue an open challenge to the theoretical community to consider how searches should be designed to yield the most astrophysically interesting upper limits. With this in mind we examine some more optimistic emission scenarios involving spin-down, and show that there are technically feasible searches, particularly for the accreting millisecond pulsars, that might place meaningful constraints on torque mechanisms. We finish with a brief discussion of prospects for indirect detection.     

太阳系天体引力对空间引力波探测日心编队构型的影响分析

针对太极空间引力波探测任务,建立了太阳系天体引力摄动对日心编队构型影响的数学模型,利用仿真手段分析了太阳系中行星和月球、矮行星和小行星引力摄动对空间引力波探测日心编队构型的影响,提出了一种综合考虑小行星到卫星轨道距离和星等的二重筛选方法,能够快速估计小行星相对加速度的上界.分析了日心编队构型卫星初始相位角变化对太阳系天...     

Variations of the gravitational field as a motive power for rhythmics of biochemical processes.

Variations of the gravitational field affected by the Sun and the Moon while the Earth's moving along the orbit seem to be a powerful source of many rhythmical processes typical of biochemical processes. Studies carried out in AARI revealed the obvious relationships between the dynamics of some biochemical reactions and lambda(D)-function describing the regular variations of the gravitational field under combined influence of the Sun and the Moon. The following of them are examined as examples: the rate of the unithiol oxidation in vitro, concentration of the thiol compounds in human urine, some hematological indicators (rate of the erythrocytes sedimentation, hemoglobin content). Compatibility of run of the biochemical indicators and lambda(D)-function is indicative of essential influence of the regular variations of the gravitational field on rhythmics of the biochemical processes. As this takes place, the solar activity acts like to the instability factor. Balance of the solar activity effects and the varying gravitational field effect alter in time depending on location in the solar activity cycle.     

The determination for ideal release point of test masses in drag-free satellites for the detection of gravitational waves

Gravitational waves are ripples in space–time predicted by Albert Einstein's general relativity and provide a new way to understand the universe. Space-borne detectors of gravitational waves, extending to very large scales, can effectively detect the middle and low-frequency gravitational wave source with the frequency band of 0.1 mHz–1 Hz. The test masses are used to make an inertial reference point in the detection of gravitational waves. Currently, there are few studies concerning the ideal release position for the test masses in the detection of gravitational waves. In this study, we give a general solution for test mass release points to minimize the relative motion between the test mass and the satellite mass center. Moreover, we discuss the situation when the release point equation is not satisfied, and the ideal release point of the along-track. Finally, we report on simulations that verify the accuracy of the theoretical derivation.     

双小行星系统引力场建模方法研究

针对弱引力双小行星系统的引力场建模问题,本文采用复杂度和精度依次递增的球体–球体模型、椭球体–球体模型和改进的限制性椭球体–椭球体模型来进行引力场建模,并分别采用椭圆积分以及无积分环节、计算效率高的二阶二次球谐函数来表征引力势,从而比较精确地刻画双小行星系统和探测器构成的限制性全三体问题的动力学模型;针对双小行星系统1999KW4,对其不同的引力场模型进行了仿真研究,分别给出了不同模型下的等效势能函数曲面及零速度曲线,比较了不同模型下的平动点位置坐标偏差。结果表明,二阶二次球谐函数计算引力势的椭球体-椭球体模型计算精度高,复杂程度低,计算量更少,计算速度更快,能够较精确的对双小行星系统进行引力场建模。     

Stacked recurrent neural network based high precision pointing coupled control of the spacecraft and telescopes

In some space missions especially in the field of space gravitational wave detection, the telescope needs to point to a certain target through attitude movement and pointing control. In several mainstream gravitational wave detection missions, the detector usually consists of a cluster of three identical satellites, flying in a quasi-equilateral triangular formation with a big edge length, so every satellite needs two telescopes to point each other and constitute three giant Michelson-Type interferometers. Therefore, a satellite platform system with two telescopes is researched in this paper. This research helps to characterize the attitude motion of a telescope for space astronomical observation or space gravitational wave detection, provides new method on the telescope’s high-precision pointing control. For this purpose, we derive a satellite-telescope coupling attitude model, design the sliding mode controller for satellite and the stacked recurrent neural network adaptive controller for telescope. In the stacked recurrent neural network adaptive controller design, a sliding mode control technology is adopted. In addition, we propose a combinatorial optimization method for network weights in the stacked recurrent neural network training process, that is, the output layer is corrected by the adaptive law, and the correction of other layers adopt the error backpropagation method. Finally, a numerical simulation method verifies the effectiveness of the controller design.     

空间引力红移实验的原理与精度

通过对文献[4, 5]关于空间引力红移实验原理与精度的分析,根据爱因斯坦惯性力与引力等效的原理,提出在航天器内部,重力的大部分被惯性力抵消,因而其中的微重力比轨道重力小很多(失重).因此,应当把星载原子钟的重力势取为与微重力相当的有效重力势,而不能简单地将星载钟的重力势取为轨道重力势.另外,检验相对论红移需要将理论值与实验值进行对比,这两种数值均具有误差,而检验精度取决于误差较大者.因此,如果不提高地球重力模型(例如EGM2008)精度而只提高测量精度则不能提高检验精度.     

Influence of the 2:1 resonance in the orbits of GPS satellites

Due to the characteristics of their orbits the GPS satellites are submitted to the following main perturbations: terrestrial gravitational field, luni-solar gravitational attraction and solar radiation pressure (including the effects of the Earth's shadow). An additional perturbation arises due to the 2:1 commensurability of the orbital period of the satellite with the period of the Earth's rotation. An analytical theory is briefly presented to solve the equations of motion including the previously mentioned effects. The analytical solution, based on the Lie-Hori method, is compared with a numerical integration of the equations.     

Dynamical stability of plasma irregularities produced by powerful radio wave in the F region of the ionosphere

The paper demonstrates that the artificial plasma irregularities in the F region of the ionosphere are dynamical structures caused by the component of temperature gradient parallel with gravitational field. The concept is justified by theoretical estimates of critical parameters of thermal convection in the heated ionospheric volume. Presented results of radar observations of small-scale irregularities are explained by the thermal convection.     

A fast Chebyshev polynomial method for calculating asteroid gravitational fields using space partitioning and cosine sampling

This paper presents a computationally fast method for solving gravitational accelerations near irregularly-shaped asteroids. This method is based on analytical three-dimensional Chebyshev polynomial approximation of the polyhedral gravity. For the purpose of improving the approximation accuracy, space partitioning schemes based on practical flight zones is used to avoid interpolation the whole space around the target asteroid. Specifically, a minimum ellipsoid close to the asteroid surface is defined to select the space for surrounding trajectories with safe distance and a cone connected to the surface is defined to select the space for descent trajectories. Moreover, interpolation points are sampled in a cosine sampling fashion according to the Chebyshev-Gauss-Lobatto nodes and a radial adaption technique. The performance of different space partitioning schemes is analyzed. The effectiveness of the proposed method is validated through simulations of solving gravitational accelerations at the test points near different shaped asteroids 1996 HW1, 433 Eros, 25143 Itokawa and 101955 Bennu.     

Orbit insertion error analysis for a space-based gravitational wave observatory

Constellation is required to be highly stable over several years for a space-based gravitational wave observatory. However, the stability of the constellation can be affected by orbit insertion errors. The effects of orbit insertion errors on the constellation are mainly studied in this paper. Firstly, Monte-Carlo, Unscented Transformation Covariance Analysis Method (UTCAM) and Spherical Simplex Unscented Transformation Covariance Analysis Method (SSUTCAM) are used for simulation. The results indicate that UTCAM and SSUTCAM are highly efficient in calculating, with a relative error of less than 6%. Therefore, it is concluded that because of their accuracy and high efficiency, UTCAM and SSUTCAM can be adequately used in orbit insertion error analysis for a space-based gravitational wave observatory. Secondly, SSUTCAM is used to study the effects of position and velocity errors on the constellation. For the case in this paper, when the position error does not exceed 300 km, and the velocity error does not exceed 4 cm/s, the constellation remains stable.     

日晕轨道卫星的转移轨道中途修正研究

由于平动点任务探测器对各种误差源和摄动因素的敏感性,因此必须考虑转移轨道的中途修正问题.以晕轨道近地点入轨的转移轨道为例,进行了初始发射误差的灵敏度分析,提出了三脉冲和四脉冲两种中途修正方案,并且讨论了转移轨道初始误差、导航误差、机动执行误差等误差源和地球摄动、月球摄动、太阳光压摄动等摄动因素对转移轨道修正代价和修正效果的影响.仿真得到了修正时刻和误差量与修正量之间的关系,Monte Carlo仿真结果表明给出的两种修正方案是可行的.     

Modeling irregular small bodies gravity field via extreme learning machines and Bayesian optimization

Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Feedforward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELM-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for asteroid 25143 Itokawa and comet 67/P Churyumov-Gerasimenko show that ELM-based SLFN are able learn the desired functional relationship both globally and in selected localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for guidance and control in close-proximity operations near the asteroid surface.     

Dynamic orbit propagation in a gravitational field of an inhomogeneous attractive body using the Lagrange coefficients

The analytical methods have nearly been replaced by the numerical methods due to their higher accuracy and accessibility of computation facilities. The semi-analytical Lagrange method of orbit propagation using f and g series is a competitive alternative to the numerical integration technique if the Lagrange coefficients are derived in a full gravitational field. In this paper, a generalization of the Lagrange method of orbit propagation is introduced. In other words, we introduce a complete form of the Lagrange coefficients in all force fields developed in the spherical harmonics for example full gravitational field of the Earth. The method is numerically compared with the numerical integration technique. In order to show the numerical performance of the method, it has been implemented for orbit propagation of a GPS-like MEO and CHAMP-like LEO satellites. Discrepancy at centimeter level for CHAMP-like and sub-millimeter accuracy for GPS-like satellites shows relatively high performance of the developed algorithm. Compared to integration method, the proposed Lagrange method is nearly faster by a factor two for small Nmax and four for large Nmax.     

Equilibrium positions on stationary orbits and planetary principal inertia axis orientations for the Solar System

We present a qualitative analysis in a phase space to determine the longitudinal equilibrium positions on the planetary stationary orbits by applying an analytical model that considers linear gravitational perturbations. We discuss how these longitudes are related with the orientation of the planetary principal inertia axes with respect to their Prime Meridians, and then we use this determination to derive their positions with respect to the International Celestial Reference Frame. Finally, a numerical analysis of the non-linear effects of the gravitational fields on the equilibrium point locations is developed and their correlation with gravity field anomalies shown.     

Effects of electrostatic forces on the vertical structure of planetary rings

We have calculated the vertical structure of planetary dust rings as it results from a balance between an electrostatic force on the dust grains and the vertical component of the gravitational force from the central planet. The electrostatic force results from the charging of the dust grains by the ambient plasma and a large scale electric field due to a shielding electric field and the resulting vertical dust distribution are strongly dependent on dust size, dust and plasma density, plasma temperature and plasma ion type. The dust density distribution has a different dependence on these parameters in tenuous and in dense dust rings. We solve the relevant equations numerically and also by linearization in the limiting cases of tenuous or dense rings. Our results indicate that the effects treated in this paper may be important in both Jupiter's and Saturn's rings.