With the rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the f...With the rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems. This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As a first step, the global solar system reference system is expressed as a multipolar expansion and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.展开更多
Based on years of input from the four geodetic techniques （SLR, GPS, VLBI and DORIS）, the strategies of the combination were studied in SHAO to generate a new global terrestrial reference frame as the material reali...Based on years of input from the four geodetic techniques （SLR, GPS, VLBI and DORIS）, the strategies of the combination were studied in SHAO to generate a new global terrestrial reference frame as the material realization of the ITRS defined in IERS Conventions. The main input includes the time series of weekly solutions （or fortnightly for SLR 1983-1993） of observational data for satellite techniques and session-wise normal equations for VLBI. The set of estimated unknowns includes 3- dimensional Cartesian coordinates at the reference epoch 2005.0 of the stations distributed globally and their rates as well as the time series of consistent Earth Orientation Parameters （EOPs） at the same epochs as the input. Besides the final solution, namely SOL-2, generated by using all the inputs before 2015.0 obtained from short-term observation processing, another reference solution, namely SOL- 1, was also computed by using the input before 2009.0 based on the same combination of procedures for the purpose of comparison with ITRF2008 and DTRF2008 and for evaluating the effect of the latest six more years of data on the combined results. The estimated accuracy of the x-component and y-component of the SOL- 1 TRF-origin was better than 0.1 mm at epoch 2005.0 and better than 0.3 mm yr- 1 in time evolution, either compared with ITRF2008 or DTRF2008. However, the z-component of the translation parameters from SOL-1 to ITRF2008 and DTRF2008 were 3.4 mm and -1.0 ram, respectively. It seems that the z-component of the SOL-1 TRF-origin was much closer to the one in DTRF2008 than the one in ITRF2008. The translation parameters from SOL-2 to ITRF2014 were 2.2, -1.8 and 0.9 mm in the x-, y- and z-components respectively with rates smaller than 0.4 mmyr-1. Similarly, the scale factor transformed from SOL-1 to DTRF2008 was much smaller than that to ITRF2008. The scale parameter from SOL-2 to ITRF2014 was -0.31 ppb with a rate lower than 0.01 ppb yr-1. The external precision （WRMS） compared with IERS EOP 08 C04 of the combined EOP series was smaller than 0.06 mas for the polar motions, smaller than 0.01 ms for the UT1-UTC and smaller than 0.02 ms for the LODs. The precision of the EOPs in SOL-2 was slightly higher than that of SOL-1.展开更多
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this un...This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.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
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
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
Considered to be extensions of the Hipparcos reference system, PPMX and UCAC3 are two of the most important astrometric catalogs released in current years. Extensive analyses of these two large catalogs have been made...Considered to be extensions of the Hipparcos reference system, PPMX and UCAC3 are two of the most important astrometric catalogs released in current years. Extensive analyses of these two large catalogs have been made in order to determine the local and overall systematic biases. The regional and magnitude dependent differences in stellar position and proper motion are comparable to random errors and are even larger in the northern hemisphere. The global orientation bias vector ε between the two systems is also significant （up to 17 mas）, which shows the overall differences of the PPMX and UCAC3 catalogs and their reference systems. On the other hand, the term for the global rotation vector a; is small （tenths of mas per year）： it is reasonable to believe that the PPMX and UCAC3 reference frames do not rotate with respect to each other. Because of plate dependent and field-to-field errors in the UCAC3 catalog, we suggest that positions and proper motions of UCAC3 stars in the northern hemisphere （δ 〉 -20°） should be used with caution.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
The Earth Orientation Parameters(EOP)provide a time-varying transition relationship between the International Terrestrial Reference Frame and the International Celestial Reference Frame.To support deep space explorati...The Earth Orientation Parameters(EOP)provide a time-varying transition relationship between the International Terrestrial Reference Frame and the International Celestial Reference Frame.To support deep space exploration and the Beidou Navigation Satellite System,the Chinese New-generation Very Long Baseline Interferometry Network(CNVN)is under construction for independent monitoring of the EOP.This paper evaluates the performance of existing 4-antenna CNVN through a batch generated observation schedules followed by extensive Monte Carlo simulations.The optimal positions of the fifth and sixth antennas of CNVN are found from 24hypothetical antenna positions uniformly distributed in China.In this process,the weighted parameters are optimized,which not only reduce the possibility of large error of EOP estimation accuracy due to unreasonable combination,but also greatly reduce the calculation cost.展开更多
基金Supported by the National Natural Science Foundation of China
文摘With the rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems. This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As a first step, the global solar system reference system is expressed as a multipolar expansion and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.
基金supported by the Ministry of Science and Technology of China(2015FY310200)the National Key Research and Development Program of China(2016YFB0501405)+1 种基金the National Natural Science Foundation of China(11173048 and 11403076)the State Key Laboratory of Aerospace Dynamics and the Crustal Movement Observation Network of China(CMONOC)
文摘Based on years of input from the four geodetic techniques （SLR, GPS, VLBI and DORIS）, the strategies of the combination were studied in SHAO to generate a new global terrestrial reference frame as the material realization of the ITRS defined in IERS Conventions. The main input includes the time series of weekly solutions （or fortnightly for SLR 1983-1993） of observational data for satellite techniques and session-wise normal equations for VLBI. The set of estimated unknowns includes 3- dimensional Cartesian coordinates at the reference epoch 2005.0 of the stations distributed globally and their rates as well as the time series of consistent Earth Orientation Parameters （EOPs） at the same epochs as the input. Besides the final solution, namely SOL-2, generated by using all the inputs before 2015.0 obtained from short-term observation processing, another reference solution, namely SOL- 1, was also computed by using the input before 2009.0 based on the same combination of procedures for the purpose of comparison with ITRF2008 and DTRF2008 and for evaluating the effect of the latest six more years of data on the combined results. The estimated accuracy of the x-component and y-component of the SOL- 1 TRF-origin was better than 0.1 mm at epoch 2005.0 and better than 0.3 mm yr- 1 in time evolution, either compared with ITRF2008 or DTRF2008. However, the z-component of the translation parameters from SOL-1 to ITRF2008 and DTRF2008 were 3.4 mm and -1.0 ram, respectively. It seems that the z-component of the SOL-1 TRF-origin was much closer to the one in DTRF2008 than the one in ITRF2008. The translation parameters from SOL-2 to ITRF2014 were 2.2, -1.8 and 0.9 mm in the x-, y- and z-components respectively with rates smaller than 0.4 mmyr-1. Similarly, the scale factor transformed from SOL-1 to DTRF2008 was much smaller than that to ITRF2008. The scale parameter from SOL-2 to ITRF2014 was -0.31 ppb with a rate lower than 0.01 ppb yr-1. The external precision （WRMS） compared with IERS EOP 08 C04 of the combined EOP series was smaller than 0.06 mas for the polar motions, smaller than 0.01 ms for the UT1-UTC and smaller than 0.02 ms for the LODs. The precision of the EOPs in SOL-2 was slightly higher than that of SOL-1.
基金supported by the National Natural Science Foundation of China (NSFC) (10872155)
文摘This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.
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funded by the National Natural Science Foundation of China(Grant No. 10973009)This research makes use of data products UCAC3 (U.S. Naval Observatory)
文摘Considered to be extensions of the Hipparcos reference system, PPMX and UCAC3 are two of the most important astrometric catalogs released in current years. Extensive analyses of these two large catalogs have been made in order to determine the local and overall systematic biases. The regional and magnitude dependent differences in stellar position and proper motion are comparable to random errors and are even larger in the northern hemisphere. The global orientation bias vector ε between the two systems is also significant （up to 17 mas）, which shows the overall differences of the PPMX and UCAC3 catalogs and their reference systems. On the other hand, the term for the global rotation vector a; is small （tenths of mas per year）： it is reasonable to believe that the PPMX and UCAC3 reference frames do not rotate with respect to each other. Because of plate dependent and field-to-field errors in the UCAC3 catalog, we suggest that positions and proper motions of UCAC3 stars in the northern hemisphere （δ 〉 -20°） should be used with caution.
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supported by the National Natural Science Foundation of China(NSFC)under grant No.42304044。
文摘The Earth Orientation Parameters(EOP)provide a time-varying transition relationship between the International Terrestrial Reference Frame and the International Celestial Reference Frame.To support deep space exploration and the Beidou Navigation Satellite System,the Chinese New-generation Very Long Baseline Interferometry Network(CNVN)is under construction for independent monitoring of the EOP.This paper evaluates the performance of existing 4-antenna CNVN through a batch generated observation schedules followed by extensive Monte Carlo simulations.The optimal positions of the fifth and sixth antennas of CNVN are found from 24hypothetical antenna positions uniformly distributed in China.In this process,the weighted parameters are optimized,which not only reduce the possibility of large error of EOP estimation accuracy due to unreasonable combination,but also greatly reduce the calculation cost.
