The adoption of the International Celestial Reference System （ICRS）, based on Very Long Baseline Interferometry （VLBI） observations of extragalactic radiosources by the International Astronomical Union （IAU） sin...The adoption of the International Celestial Reference System （ICRS）, based on Very Long Baseline Interferometry （VLBI） observations of extragalactic radiosources by the International Astronomical Union （IAU） since 1998 January 1, opened a new era for astronomy. The ICRS and the corresponding frame, the International Celestial Reference Frame （ICRF）, replaced the Fundamental Catalog （FK5） based on positions and proper motions of bright stars, with the Hipparcos cat- alog being adopted as the primary realization of the ICRS in optical wavelengths. According to its definition, the ICRS is such that the barycentric directions of distant extragalactic objects show no global rotation with respect to these objects; this pro- vides a quasi-inertial reference for measuring the positions and angular motions of the celestial objects. Other resolutions on reference systems were passed by the IAU in 2000 and 2006 and endorsed by the International Union of Geodesy and Geophysics （IUGG） in 2003 and 2007, respectively. These especially concern the definition and re- alization of the astronomical reference systems in the framework of general relativity and transformations between them. First, the IAU 2000 resolutions refined the con- cepts and definition of the astronomical reference systems and parameters for Earth＇s rotation, and adopted the IAU 2000 precession-nutation. Then, the IAU 2006 resolutions adopted a new precession model that is consistent with dynamical theories; they also addressed definition, terminology or orientation issues relative to reference systems and time scales that needed to be specified after the adoption of the IAU 2000 resolutions. An additional IUGG 2007 resolution defined the International Terrestrial Reference System （ITRS） so that it strictly complies with the IAU recommendations. Finally, the IAU 2009 resolutions adopted a new system of astronomical constants and an improved realization of the ICRF. These fundamental changes have led to significant improvements in the fields of astrometry, celestial mechanics, geodynam- ics, geodesy, etc. Of special interest are the improvements in the model for variations in Earth＇s rotation, which, in turn, can provide better knowledge of the dynamics of the Earth＇s interior. These have also contributed to a significant improvement in the accuracy of the ephemerides of the solar system bodies as determined from modern measurements, with a large number of scientific applications. This paper recalls the main aspects of the recent IAU resolutions on reference systems as well as their con- sequences on the concepts, definitions, nomenclature and models that are suitable for the definition, realization and transformation of reference frames at a microarcsecond level.展开更多
This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then ...This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.展开更多
In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. F...In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.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
We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the ...We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.展开更多
We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their orbits.The system is stable if there is no exchange or cross of orbits.Starting from the Sundman i...We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their orbits.The system is stable if there is no exchange or cross of orbits.Starting from the Sundman inequality,the equation of the kinematical boundaries is derived.We discuss a reasonable situation,where two planets with known orbits are more massive than the third one.The boundaries of possible motions are controlled by the parameter c^2E.If the actual value of c^2E is less than or equal to a critical value(c^2 E)cr,then the regions of possible motions are bounded and therefore the system is stable.The criteria obtained in special cases are applied to the Solar System and the currently known extrasolar planetary systems.Our results are checked using N-body integrator.展开更多
With tremendous advances in modem techniques, Einstein＇s general rela- tivity has become an inevitable part of deep space missions. We investigate the rela- tivistic algorithm for time transfer between the proper tim...With tremendous advances in modem techniques, Einstein＇s general rela- tivity has become an inevitable part of deep space missions. We investigate the rela- tivistic algorithm for time transfer between the proper time - of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard com- puter because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.展开更多
Object correlation and maneuver detection are persistent problems in space surveillance and maintenance of a space object catalog. We integrate these two prob- lems into one interrelated problem, and consider them sim...Object correlation and maneuver detection are persistent problems in space surveillance and maintenance of a space object catalog. We integrate these two prob- lems into one interrelated problem, and consider them simultaneously under a sce- nario where space objects only perform a single in-track orbital maneuver during the time intervals between observations. We mathematically formulate this integrated sce- nario as a maximum a posteriori （MAP） estimation. In this work, we propose a novel approach to solve the MAP estimation. More precisely, the corresponding posterior probability of an orbital maneuver and a joint association event can be approximated by the Joint Probabilistic Data Association （JPDA） algorithm. Subsequently, the ma- neuvering parameters are estimated by optimally solving the constrained non-linear least squares iterative process based on the second-order cone programming （SOCP） algorithm. The desired solution is derived according to the MAP criterions. The per- formance and advantages of the proposed approach have been shown by both theoret- ical analysis and simulation results. We hope that our work will stimulate future work on space surveillance and maintenance of a space object catalog.展开更多
Concerns for the collision risk involving Starlink satellites have motivated the interest in obtaining their accurate orbit knowledge.However,accurate orbit determination(OD)and prediction(OP)of Starlink satellites co...Concerns for the collision risk involving Starlink satellites have motivated the interest in obtaining their accurate orbit knowledge.However,accurate orbit determination(OD)and prediction(OP)of Starlink satellites confront two main challenges:mismatching or missed matching of sparse tracklets to maneuvering satellites,and unknown or unmodeled orbit maneuvers.How to exactly associate a tracklet to the right satellite is the primary issue,since a maneuvering satellite does not follow the naturally evolving orbit during the maneuvering,while more tracklets are needed for developing an accurate orbit maneuver model.If these two challenges are not well addressed,it may lead to catalog maintenance failure or even loss of objects.This paper proposes a method to correctly match tracklets to the climbing Starlink satellites.It is based on the recursive OD and OP,in which the orbit maneuver is modeled and the thrust is estimated,such that the subsequent OP accuracy guarantees the correct match of tracklets shortly after the OD time.Experiments with climbing Starlink satellites demonstrate that the tracklets within three days of the last TLE(two-line element)are all correctly matched to the right satellites.With the matched tracklets,the thrust accelerations of climbing Starlink satellites can be precisely estimated through an orbit control approach,and the position prediction accuracy over 48 hours is at the level of a few kilometers,providing accurate orbit knowledge for reliable collision warning involving Starlink satellites.展开更多
文摘The adoption of the International Celestial Reference System （ICRS）, based on Very Long Baseline Interferometry （VLBI） observations of extragalactic radiosources by the International Astronomical Union （IAU） since 1998 January 1, opened a new era for astronomy. The ICRS and the corresponding frame, the International Celestial Reference Frame （ICRF）, replaced the Fundamental Catalog （FK5） based on positions and proper motions of bright stars, with the Hipparcos cat- alog being adopted as the primary realization of the ICRS in optical wavelengths. According to its definition, the ICRS is such that the barycentric directions of distant extragalactic objects show no global rotation with respect to these objects; this pro- vides a quasi-inertial reference for measuring the positions and angular motions of the celestial objects. Other resolutions on reference systems were passed by the IAU in 2000 and 2006 and endorsed by the International Union of Geodesy and Geophysics （IUGG） in 2003 and 2007, respectively. These especially concern the definition and re- alization of the astronomical reference systems in the framework of general relativity and transformations between them. First, the IAU 2000 resolutions refined the con- cepts and definition of the astronomical reference systems and parameters for Earth＇s rotation, and adopted the IAU 2000 precession-nutation. Then, the IAU 2006 resolutions adopted a new precession model that is consistent with dynamical theories; they also addressed definition, terminology or orientation issues relative to reference systems and time scales that needed to be specified after the adoption of the IAU 2000 resolutions. An additional IUGG 2007 resolution defined the International Terrestrial Reference System （ITRS） so that it strictly complies with the IAU recommendations. Finally, the IAU 2009 resolutions adopted a new system of astronomical constants and an improved realization of the ICRF. These fundamental changes have led to significant improvements in the fields of astrometry, celestial mechanics, geodynam- ics, geodesy, etc. Of special interest are the improvements in the model for variations in Earth＇s rotation, which, in turn, can provide better knowledge of the dynamics of the Earth＇s interior. These have also contributed to a significant improvement in the accuracy of the ephemerides of the solar system bodies as determined from modern measurements, with a large number of scientific applications. This paper recalls the main aspects of the recent IAU resolutions on reference systems as well as their con- sequences on the concepts, definitions, nomenclature and models that are suitable for the definition, realization and transformation of reference frames at a microarcsecond level.
文摘This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.
文摘In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.
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.
基金Supported by the National Natural Science Foundation of China
文摘We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.
基金the National Natural Science Foundation of China(Grant Nos.11772167 and 11822205)。
文摘We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their orbits.The system is stable if there is no exchange or cross of orbits.Starting from the Sundman inequality,the equation of the kinematical boundaries is derived.We discuss a reasonable situation,where two planets with known orbits are more massive than the third one.The boundaries of possible motions are controlled by the parameter c^2E.If the actual value of c^2E is less than or equal to a critical value(c^2 E)cr,then the regions of possible motions are bounded and therefore the system is stable.The criteria obtained in special cases are applied to the Solar System and the currently known extrasolar planetary systems.Our results are checked using N-body integrator.
基金Supported by the National Natural Science Foundation of China
文摘With tremendous advances in modem techniques, Einstein＇s general rela- tivity has become an inevitable part of deep space missions. We investigate the rela- tivistic algorithm for time transfer between the proper time - of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard com- puter because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.
文摘Object correlation and maneuver detection are persistent problems in space surveillance and maintenance of a space object catalog. We integrate these two prob- lems into one interrelated problem, and consider them simultaneously under a sce- nario where space objects only perform a single in-track orbital maneuver during the time intervals between observations. We mathematically formulate this integrated sce- nario as a maximum a posteriori （MAP） estimation. In this work, we propose a novel approach to solve the MAP estimation. More precisely, the corresponding posterior probability of an orbital maneuver and a joint association event can be approximated by the Joint Probabilistic Data Association （JPDA） algorithm. Subsequently, the ma- neuvering parameters are estimated by optimally solving the constrained non-linear least squares iterative process based on the second-order cone programming （SOCP） algorithm. The desired solution is derived according to the MAP criterions. The per- formance and advantages of the proposed approach have been shown by both theoret- ical analysis and simulation results. We hope that our work will stimulate future work on space surveillance and maintenance of a space object catalog.
基金supported by the National Natural Science Foundation of China(Grant Nos.12103035 and 41874035)the Fundamental Research Funds for the Central Universities,China(Grant No.2042021kf0001)。
文摘Concerns for the collision risk involving Starlink satellites have motivated the interest in obtaining their accurate orbit knowledge.However,accurate orbit determination(OD)and prediction(OP)of Starlink satellites confront two main challenges:mismatching or missed matching of sparse tracklets to maneuvering satellites,and unknown or unmodeled orbit maneuvers.How to exactly associate a tracklet to the right satellite is the primary issue,since a maneuvering satellite does not follow the naturally evolving orbit during the maneuvering,while more tracklets are needed for developing an accurate orbit maneuver model.If these two challenges are not well addressed,it may lead to catalog maintenance failure or even loss of objects.This paper proposes a method to correctly match tracklets to the climbing Starlink satellites.It is based on the recursive OD and OP,in which the orbit maneuver is modeled and the thrust is estimated,such that the subsequent OP accuracy guarantees the correct match of tracklets shortly after the OD time.Experiments with climbing Starlink satellites demonstrate that the tracklets within three days of the last TLE(two-line element)are all correctly matched to the right satellites.With the matched tracklets,the thrust accelerations of climbing Starlink satellites can be precisely estimated through an orbit control approach,and the position prediction accuracy over 48 hours is at the level of a few kilometers,providing accurate orbit knowledge for reliable collision warning involving Starlink satellites.
