Theoretical and numerical studies of rock breaking mechanism by double disc cutters

A plane mechanical model of rock breaking process by double disc cutter at the center of the cutterhead is established based on contact mechanics to analyze the stress evolution in the rock broken by cutters with different spacings. A continuous-discontinuous coupling numerical method based on zero-thickness cohesive elements is developed to simulate rock breaking using double cutters. The process, mechanism,and characteristics of rock breaking are comprehensively analyzed from five aspects: peak force, breaking form, breaking efficiency, crack mode, and breaking degree. The results show that under the penetrating action of cutters, dense cores are formed due to shear failure under respective cutters. The tensile cracks propagate in the rock, and then rock chips form with increasing penetration depth. When the cutter spacing is increased from 10 to 80 mm, the peak force gradually increases, the rock breaking range increases first and then decreases, the specific energy decreases first and then rises, and the breaking coefficient of intermediate rock decreases from 0.955 to 0.788. The area of rock breaking is positively correlated with the length of the tensile crack. Furthermore, the length of the tensile crack accounts for 14.4%–33.6% of the total crack length.

A method for calculating probability of collision between space objects

A method is developed to calculate probability of collision. Based on geometric features of space objects during the encounter, it is reasonable to separate the radial orbital motions from those in the cross section for most encounter events that occur in a near-circular orbit. Therefore, the probability of collision caused by differences in both altitude of the orbit in the radial direction and the probability of collision caused by differences in arrival time in the cross section are calculated. The net probability of collision is expressed as an explicit expression by multiplying the above two components. Numerical cases are applied to test this method by comparing the results with the general method. The results indicate that this method is valid for most encounter events that occur in near-circular orbits.

Experiment on diffuse reflection laser ranging to space debris and data analysis

Space debris poses a serious threat to human space activities and needs to be measured and cataloged. As a new technology for space target surveillance, the measurement accuracy of diffuse reflection laser ranging （DRLR） is much higher than that of microwave radar and optoelectronic measurement. Based on the laser ranging data of space debris from the DRLR system at Shanghai Astronomical Observatory acquired in March-April, 2013, the characteristics and precision of the laser ranging data are analyzed and their applications in orbit determination of space debris are discussed, which is implemented for the first time in China. The experiment indicates that the precision of laser ranging data can reach 39 cm-228 cm. When the data are sufficient enough （four arcs measured over three days）, the orbital accuracy of space debris can be up to 50 m.

Electromagnetic effects on the orbital motion of a charged spacecraft

This paper deals with the effects of electromagnetic forces on the orbital motion of a spacecraft. The electrostatic charge which a spacecraft generates on its surface in the Earth＇s magnetic field will be subject to a perturbative Lorentz force. A model incorporating all Lorentz forces as a function of orbital elements has been developed on the basis of magnetic and electric fields. This Lorentz force can be used to modify or perturb the spacecraft＇s orbits. Lagrange＇s planetary equations in the Gauss variational form are derived using the Lorentz force as a perturbation to a Keplerian orbit. Our approach incorporates orbital inclination and the true anomaly. The numer- ical results of Lagrange＇s planetary equations for some operational satellites show that the perturbation in the orbital elements of the spacecraft is a second order perturba- tion for a certain value of charge. The effect of the Lorentz force due to its magnetic component is three times that of the Lorentz force due to its electric component. In addition, the numerical results confirm that the strong effects are due to the Lorentz force in a polar orbit, which is consistent with realistic physical phenomena that occur in polar orbits. The results confirm that the magnitude of the Lorentz force depends on the amount of charge. This means that we can use artificial charging to create a force to control the attitude and orbital motion of a spacecraft.

The transformation between τ and TCB for deep space missions under IAU resolutions

For tracking spacecraft and performing radio science, the transformation between the proper time （τ） given by a clock carried onboard a spacecraft and the barycentric coordinate time （TCB） is investigated under IAU resolutions. In order to more clearly demonstrate manifestations of a physical model and improve computa- tional efficiency, an analytic approach is adopted. After numerical verification, it is confirmed that this method is adequate to describe a Mars orbiter during one year, and is particularly good at describing the influence from perturbing bodies. Further analyses demonstrate that there are two main effects in the transformation： the gravi- tational field of the Sun and the velocity of the spacecraft in the barycentric coordinate reference system. The combined contribution of these effects is at the level of a few sub-seconds.

Attitude dynamics and control of spacecraft using geomagnetic Lorentz force

Attitude stabilization of a charged rigid spacecraft in Low Earth Orbit using torques due to Lorentz force in pitch and roll directions is considered. A spacecraft that generates an electrostatic charge on its surface in the Earth’s magnetic field will be subject to perturbations from the Lorentz force. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft’s orientation. We assume that the spacecraft is moving in the Earth’s magnetic field in an elliptical orbit under the effects of gravitational, geomagnetic and Lorentz torques. The magnetic field of the Earth is modeled as a non-tilted dipole.A model incorporating all Lorentz torques as a function of orbital elements has been developed on the basis of electric and magnetic fields. The stability of the spacecraft orientation is investigated both analytically and numerically. The existence and stability of equilibrium positions is investigated for different values of the charge to mass ratio（α＊）. Stable orbits are identified for various values of α＊. The main parameters for stabilization of the spacecraft are α＊and the difference between the components of the moment of inertia for the spacecraft.

A Novel Ephemeris Model for Martian Moons Incorporating Their Free Rotation

High-precision ephemerides not only support space missions,but can also be used to study the origin and future of celestial bodies.In this paper,a coupled orbit-rotation dynamics model that fully takes into account the rotation of the Martian moons is developed.Phobos and Deimos’rotations are first described by Eulerian rotational equations,and integrated simultaneously with the orbital motion equations.Orbital and orientational parameters of Mars satellites were simultaneously obtained by numerical integration for the first time.In order to compare the differences between our newly developed model and the one now used in the ephemerides,we first reproduced and simulated the current model using our own parameters,and then fit it to the Institut de Mécanique Céleste et de Calcul deséphémérides ephemerides using least-square procedures.The adjustment test simulations show Phobos and Deimos’orbital differences between the refined model and the current model are no more than 300 m and125 m,respectively.The orientation parameters are confirmed and the results are in good agreement with the International Astronomical Union results.Moreover,we simulated two perturbations(main asteroids and mutual torques)which were not included in our refined model,and find that their effects on the orbits are completely negligible.As for the effect on rotation,we propose to take care of the role of mutual attraction in future models.

Feasible region and stability analysis for hovering around elongated asteroids with low thrust

This paper investigates properties of low-thrust hovering, including the feasible region and stability, in terms of the dynamical parameters for elongated asteroids. An approximate rotating mass dipole model, by which the description of the rotational gravitational field is reduced to two independent parameters, is employed to construct normalized dynamical equations. The boundaries of the feasible region are determined by contours representing the magnitude of the active control. The effects of a rotating gravitational field and maximal magnitude of the low thrust on the feasible hovering regions are analyzed with numerical results. The stability conditions are derived according to the forms of the eigenvalues of the linearized equation near the hovering position. The stable regions are then determined by a grid search and the effects of the relevant parameters are analyzed in a parametric way. The results show that a close hovering can be easier to realize near the middle of the asteroid than near the two ends in the sense of both required control magnitude and stability.

The effect of f(T) gravity on an interplanetary clock and its time transfer link

As an extension of the＂teleparallel＂equivalent of general relativity,f（T）gravity is proposed to explain some puzzling cosmological behaviors,such as accelerating expansion of the Universe.Given the fact that modified gravity also has impacts on the Solar System,we might test it during future interplanetary missions with ultrastable clocks.In this work,we investigate the effects of f（T）gravity on the dynamics of the clock and its time transfer link.Under these influences,theΛ-term and theα-term of f（T）gravity play important roles.Here,Λis the cosmological constant andαrepresents a model parameter in f（T）gravity that determines the divergence from teleparallel gravity at the first order approximation.We find that the signal of f（T）gravity in the time transfer is much more difficult to detect with the current state of development for clocks than those effects on dynamics of an interplanetary spacecraft with a bounded orbit with parameters 0.5 au≤a≤5.5 au and 0≤e≤0.1.

Relativistic transformation between τ and TCB for Mars missions: Fourier analysis on its accessibility with clock offset

In the context of the fact that Einstein＇s general relativity has become an inevitable part of deep space missions, we will extend previous works on relativistic transformation between the proper time ^- of a clock onboard a spacecraft orbiting Mars and the Barycentric Coordinate Time （TCB） by taking the clock offset into ac- count and investigate its accessibility by Fourier analysis on the residuals after fitting the ^--TCB curve in terms of n-th order polynomials. We find that if the accuracy of a clock can achieve better than ~ 10-5 s or ~ 10-6 s （depending on the type of clock offset） in one year after calibration, the relativistic effects on the difference between 7- and TCB will need to be carefully considered.

Asteroid body-fixed hovering using nonideal solar sails

The problem of body-fixed hovering over an asteroid using a compact form of nonideal solar sails with a controllable area is investigated. Nonlinear dynamic equations describing the hovering problem are constructed for a spherically symmet- ric asteroid. Numerical solutions of the feasible region for body-fixed hovering are obtained. Different sail models, including the cases of ideal, optical, parametric and solar photon thrust, on the feasible region is studied through numerical simulations. The influence of the asteroid spinning rate and the sail area-to-mass ratio on the feasi- ble region is discussed. The required orientations for the sail and their corresponding variable lightness numbers are given for different hovering radii to identify the feasible region of the body-fixed hovering. An attractive scenario for a mission is introduced to take advantage of solar sail hovering.

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

The attitude dynamics of a rigid artificial satellite subject to a gravity gradient and Lorentz torques in a circular orbit are considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite＇s surface. We assume that the satellite is moving in a Low Earth Orbit in the geomagnetic field, which is considered to be a dipole. Our model of torque due to the Lorentz force is developed for an artificial satellite with a general shape, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and conditions for their existence are obtained.The numerical results show that the charge q and radius ρ0of the center of charge for the satellite provide a certain type of semi-passive control for the attitude of the satellite. The technique for this kind of control would be to increase or decrease the electrostatic screening on the satellite. The results obtained confirm that the change in charge can affect the magnitude of the Lorentz torque, which can also affect control of the satellite. Moreover, the relationship between magnitude of the Lorentz torque and inclination of the orbit is investigated.

Long-term effects of main-body's obliquity on satellite formation perturbed by third-body gravity in elliptical and inclined orbit

A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.

基于SLR精密轨道的天文定位精度分析

利用全球卫星激光测距服务系统(ILRS,International Laser Ranging Service)标准点资料对Ajisai卫星进行精密定轨,残差均方根(RMS)优于3 cm,得到该星的精密轨道.进而对长春站40 cm空间碎片光电望远镜获得的Ajisai卫星的天文定位资料进行精度分析,外符合精度约3″左右.单独利用天文定位数据进行轨道改进,内符合精度优于3″.改进轨道的x、y、z坐标3分量在观测数据覆盖范围内的精度在100 m之内.同样地对Jason-1卫星作数据分析,结果和Ajisai卫星精度相当.分析各个弧段的精度变化,发现定标星个数减少,会导致天文定位精度下降.据此提出可以把最少定标星比例作为评定数据质量的参考指标之一.

灰色模型修正及其在实时GPS卫星钟差预报中的应用研究

在GPS实时精密单点定位中,卫星钟差的实时可靠预报是实现GPS实时高精度单点定位的关键之一.星载GPS原子钟频率高,非常敏感,极易受到外界及其本身因素的影响,从而很难掌握其复杂细致的变化规律,这些属性符合灰色系统理论的特点.因此,考虑将钟差的变化过程看作一个灰色系统.在探讨二次多项式和灰色模型卫星钟差预报局限性基础上,提出了利用改进的灰色模型实时预报GPS卫星钟差的研究,最后利用3个不同时段的GPS卫星钟差资料进行不同采样间隔钟差预报精度分析、灰色模型指数系数与预报精度的关系、与二次多项式预报精度比较分析,总结不同卫星钟差类型与模型指数系数的一般关系,并与IGS最终钟差星历产品比较,验证本文提出的改进预报模型的可行性和有效性.为实时GPS动态精密单点定位提供较高精度的卫星钟差产品.

主带小行星深空探测可接近性与多目标探测轨道的实现

小行星探测是当前深空探测的热点之一,探测目标的可接近性又是探测任务首先要解决的问题.根据直接转移轨道方式下太阳系中可以探测到的区域和小行星的空间分布,确认发射能量C_3=50 km^2/s^2的直接转移轨道,可以探测大部分主带小行星;使用少量的速度修正还能够实现多目标飞越任务.同时指出,这种多目标的飞越可以达到△V-EGA轨道方案中的深空机动同样的效果,经地球引力助推,以较小能量实现小行星伴飞或更遥远小行星的探测;据此提出了一个探测器先飞越多颗主带小行星,然后借助地球引力助推探测更遥远小行星的轨道设计方案,并给出了设计实例.

SGP4/SDP4模型精度分析

本文基于最新发布的SGP4/SDP4(Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)模型设计了一套定轨方案,从空间目标库中挑选出不同类型和轨道参数的1120个目标进行计算,定量给出了SGP4/SDP4模型处理不同类型空间目标的定轨预报精度.结果表明:近地目标定轨精度为百米量级;半同步和同步轨道定轨精度平均为0.7和1.9km。椭圆轨道目标的定轨精度与偏心率有关,除少数e>0.8的椭圆轨道目标,绝大多数椭圆轨道目标定轨误差均小于10km。用SGP4/SDP4模型对近地目标预报3天,半同步轨道预报30天,同步轨道预报15天,椭圆轨道预报1天,预报误差一般不超过40km。

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.

太阳辐射指数F_(10.7)的中期预报方法

在低轨卫星的轨道计算中需要输入太阳辐射指数,它常用来描述太阳活动对高层大气密度的直接影响以及对轨道摄动的间接影响.因此太阳辐射指数的精度将影响轨道预报的精度.以太阳活动27 d短期震荡规律为基础,研究了一种利用135 d的辐射指数历史数据对F_(10.7)进行54 d中期预报的方法,能够预测太阳在未来2个自转周内辐射指数的变化.通过与其他预报方法的比较,表明:(1)该方法显著优于传统的三角函数长期预报法;(2)短期预报7 d时方法略优于美国空间天气预报中心(Space Weather Prediction Center,SWPC)的方法,RMS(Root Mean Square)下降约19%;(3)中期预报27 d时该方法与国内常用的54阶自回归模型精度基本相当,但方法的参数和需要的历史资料都明显减少,在轨道计算中使用更为简便,而且精度稳定,在54 d时预报值和实测值之间的相关系数仍然优于0.92.该方法的特点是只利用辐射指数较少的历史资料,不需要额外的太阳观测资料作支撑,能进行长达54 d的中期预报,为航天任务中的轨道中短期预报提供合理、可靠的辐射指数.

基于遗传算法的极短弧定轨

空间目标的巡天观测获取了海量的极短弧观测数据,而经典初轨计算方法对于极短弧几乎不能获得合理的结果.将初轨计算问题转换为两个三变量的分层优化问题,采用遗传算法,针对具体问题选择了优化变量以及相应的遗传操作,建立了一种极短弧初轨计算方法.基于实测资料的数值实验表明,方法可为后续工作提供有效的初值.