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 （D...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.展开更多
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 f...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.展开更多
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...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.展开更多
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...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.展开更多
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...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.展开更多
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 modif...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.展开更多
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 fo...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.展开更多
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...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.展开更多
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 orbi...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.展开更多
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...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。展开更多
基金Supported by the National Natural Science Foundation of China
文摘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.
基金Supported by the National Natural Science Foundation of China
文摘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.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 11372150)the National Basic Research Program of China (973 Program, 2012CB720000)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No. 11103010)funded by the Natural Science Foundation of China (Grant No. 11103085)+3 种基金the Fundamental Research Program of Jiangsu Province of China (Grant No. BK20131461Grant No. BK2011553)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110091120003)the Fundamental Research Funds for the Central Universities (No. 1107020116)
文摘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.
基金supported by the National Basic Research Program of China (973 Program,2012CB720000)the Tsinghua University Initiative Scientific Research Program (No.20131089268)
文摘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.
文摘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.
文摘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.
文摘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。
