Astronomical relativistic reference systems with multipolar expansion: the global one

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.

The Application of Permanent Magnet Synchronous Motor with Small Electrical Time Constant in Fiber Positioner

With the development of cutting-edge multi-object spectrographs,fiber positioners located in the focal plane are being scaled down in size,and miniature hollow-cup Permanent Magnet motors are now being considered as a suitable replacement for Faulhaber Precistep stepper motors.However,the small electrical time constant of such coreless motors poses a challenge,as the problem of severe commutation torque ripple in a fiber positioner running a position loop has been tricky.To overcome this challenge,it is advised to increase the Pulse Width Modulation(PWM)frequency as much as possible to mitigate the effects of the current fluctuation.This must be done while ensuring adequate resolution of the PWM generator.By employing a voltage open-loop field-oriented control based on a modulation frequency of 1 MHz,the drive current only costs 25 m A under a 3.3 V power supply.The sine degree of phase current is immaculate,and the repeat positioning accuracy can reach 2μm.Moreover,it is possible to further shrink the bill of devices and the layout area of the Printed Circuit Board,especially in sizesensitive applications.This device has been developed under the new generation of The Large Sky Area MultiObject Fiber Spectroscopic Telescope.

Combination of terrestrial reference frames based on space geodetic techniques in SHAO:methodology and main issues

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.

Micro-arcsecond Celestial Reference Frames:definition and realization——Impact of the recent IAU Resolutions

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.

Systematic differences in position and proper-motion between the PPMX and UCAC3 catalogs

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.

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.

Relativistic transformation between τ and TCG for Mars missions under IAU Resolutions

Considering the fact that the general theory of relativity has become an in- extricable part of deep space missions, we investigate the relativistic transformation between the proper time of an onboard clock τ and the Geocentric Coordinate Time （TCG） for Mars missions. By connecting τ with this local timescale associated with the Earth, we extend previous works which focus on the transformation between τ and the Barycentric Coordinate Time （TCB）. （TCB is the global coordinate time for the whole solar system.） For practical convenience, the relation between τ and TCG is recast to directly depend on quantities which can be read from ephemerides. We find that the difference between τ and TCG can reach the level of about 0.2 seconds in a year. To distinguish various sources in the transformation, we numerically calculate the contributions caused by the Sun, eight planets, three large asteroids and the space- craft. It is found that if the threshold of 1 microsecond is adopted, this transformation must include effects due to the Sun, Venus, the Moon, Mars, Jupiter, Saturn and the velocities of the spacecraft and Earth.

Relativistic algorithm for time transfer in Mars missions under IAU Resolutions: an analytic approach

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.

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.

Relativistic transformations between global and local velocities of an orbiter under IAU Resolutions

Einstein＇s general relativity （GR） has become an inevitable part of deep space missions. According to the International Astronomical Union （IAU） Resolutions which are built in the framework of GR, several time scales and reference systems are recommended to be used in the solar system for control, navigation and scientific op- eration of a spacecraft. Under the IAU Resolutions, we derive the transformations be- tween global and local velocities of an arbitrary orbiter. These transformations might be used in orbit determination with Doppler tracking and prediction of Doppler ob- servables for the spacecraft. Taking the YingHuo-1 Mission as a technical example of future Chinese Mars explorations, we evaluate the significance and contributions of various components in the transformations. The largest contribution of the relativistic parts in the transformations can reach the level of ～ 5 × 10-5 m s^-1. This suggests that, for such a spacecraft like we have assumed, if the accuracy of Doppler tracking is better than ～ 5 × 10-5 m s^-1 then the relativistic parts of the transformations of velocities will be required.

Weekly inter-technique combination of SLR,VLBI,GPS and DORIS at the solution level

Constructing and maintaining a stable terrestrial reference frame （TRF） is one of the key objectives of fundamental astronomy and geodesy. The datum realization for all the global TRF versions, such as ITRF2014 and its predecessor ITRF2008, assumes linear time evolution for transformation parameters and then imposes some conditions on these Helmert transformation parameters. In this paper, we investigate a new approach, which is based on weekly estimation of station positions and Helmert transformation parameters from a combination of the solutions of four space-geodetic techniques, i.e., Satellite Laser Ranging （SLR）, Very Long Baseline Interferometry （VLBI）, Global Positioning System （GPS） and Doppler Orbitography and Radiopositioning Integrated by Satellite （DORIS）. For this study, an interval of one week is chosen because the arc length of the SLR solutions is seven days. The major advantage of this weekly estimated reference frame is that both the non-linear station motions and the non-linear origin motion are implicitly taken into account. In order to study the non-linear behavior of station motions and physical parameters, ITRF2008 is used as a reference. As for datum definition of weekly reference frame, on one hand SLR is the unique technique to realize the origin and determine the scale together with VLBI, and on the other hand the orientation is realized via no net rotation with respect to ITRF2005 on a subset of core stations. Given the fact that without enough collocations an inter-technique combined TRF could not exist, the selection and relative weight of local ties surveyed at co-location sites are critical issues. To get stable results, we first assume that, if there were no events such as equipment changes between the measurement epoch of the local tie and that of the space- geodetic solution, the relative position between the two co-located stations should be invariant and this local tie could be used for computing the inter-technique combined reference flame in those weeks during the stable period of this tie. The resulting time series of both station positions and transformation parameters are studied in detail and are compared with ITRF2008. The residual station positions in the weekly combined reference frame are usually in the range of two millimeters without any periodic characteristic, but the residual station positions, when subtracting the regularized station position in ITRF2008, may reach a magnitude of a few centimeters and seem to have a significant annual signal. The physical parameter series between the weekly reference frame and ITRF2008 also show the obvious existence of an annual signal and reach a magnitude of one centimeter for origin motion and two parts per billion （ppb） for scale.

Relativistic time transfer for a Mars lander:from proper time to Areocentric Coordinate Time

As the first step in relativistic time transfer for a Mars lander from its proper time to the time scale at the ground station, we investigate the transformation between proper time and Areocentric Coordinate Time （TCA） in the framework of IAU Resolutions. TCA is a local time scale for Mars, which is analogous to the Geocentric Coordinate Time （TCG） for Earth. This transformation contains two contributions： inter- hal and external. The internal contribution comes from the gravitational potential and the rotation of Mars. The external contribution is due to the gravitational fields of other bodies （except Mars） in the Solar System. When the （in）stability of an onboard clock is assumed to be at the level of 10-13, we find that the internal contribution is dominated by the gravitational potential of spherical Mars with necessary corrections asso- ciated with the height of the lander on the areoid, the dynamic form factor of Mars, the flattening of the areoid and the spin rate of Mars. For the external contribution, we find the gravitational effects from other bodies in the Solar System can be safely neglected in this case after calculating their maximum values.

Relativistic time transfer for a Mars lander： from Areocentric CoordinateTime to Barycentric Coordinate Time

As the second step of relativistic time transfer for a Mars lander,we investigate the transformation between Areocentric Coordinate Time（TCA）and Barycentric Coordinate Time（TCB）in the framework of IAU Resolutions.TCA is a local time scale for Mars,which is analogous to the Geocentric Coordinate Time（TCG）for Earth.This transformation has two parts:contributions associated with gravitational bodies and those depending on the position of the lander.After setting the instability of an onboard clock to 10;and considering that the uncertainty in time is about 3.2 microseconds after one Earth year,we find that the contributions of the Sun,Mars,Jupiter and Saturn in the leading term associated with these bodies can reach a level exceeding the threshold and must be taken into account.Other terms can be safely ignored in this transformation for a Mars lander.

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.

Quasars in the Galactic Anti-Center Area from LAMOST DR3

Abstract We present a sample of quasars discovered in an area near the Galactic Anti-Center covering 150°≤l≤ 210° and ｜b｜ ≤ 30°, based on LAMOST Data Release 3 （DR3）. This sample contains 151 spectroscopically confirmed quasars. Among them 80 are newly discovered with LAMOST. All these quasars are very bright, with i magnitudes peaking around 17.5 mag. All the new quasars were discovered serendipitously from objects that were originally targeted with LAMOST as stars having bluer colors, except for a few candidates targeted as variable, young stellar objects. This bright quasar sample at low Galactic latitudes will help fill the gap in the spatial distribution of known quasars near the Galactic disk that are used to construct an astrometric reference frame for the purpose of accurate proper motion measurements that can be applied to, for example, Gala. They are also excellent tracers to probe the kinematics and chemistry of the interstellar medium in the Milky Way disk and halo via absorption line spectroscopy.

Black Sun: Ocular Invisibility of Relativistic Luminous Astrophysical Bodies

Considered as a gedanken experiment are the conditions under which the relativistic Doppler shifting of visible electromagnetic radiation to beyond the human ocular range could reduce the incident radiance of the source, and render a luminous astrophysical body (LAB) invisible to a naked eye. This paper determines the proper distance as a function of relativistic velocity at which a luminous object attains ocular invisibility.

Two New Control Signal Approaches for Obtaining the MRAS-CDM and a Real-time Application

The coefficient diagram method （CDM） is one of the most effective control design methods. It creates control systems that are very stable and robust with responses without the overshoot and small settling time. Furthermore, all control parameters of the control systems are changed by varying some adjustment parameters in CDM depending on the demands. The model reference adaptive systems （MRAS） are the systems that follow and change the control parameters according to a given model reference system. There are several methods to combine the CDM with MRAS. One of these is to use the MRAS parameters as a gain of the CDM parameters. Another is to directly use the CDM parameters as the MRAS parameters. In the industrial applications, the system parameters can be changed frequently, but if the controller, by self-tuning, recalculates and develops its own parameters continuously, the system becomes more robust. Also, if the poles of the controlled systems approach the jw axis, the response of the closed-loop MRAS becomes more and more insufficient. In order to obtain better results, CDM is combined with a self-tuning model reference adaptive system. Systems controlled by a model reference adaptive controller give responses with small or without overshoot, have small settling times, and are more robust. Thus, in this paper, a hybrid combination of MRAS and CDM is developed and two different control structures of the control signal are investigated. The two methods are compared with MRAS and applied to real-time process control systems.

Area and shape distortions in open-source discrete global grid systems

A Discrete Global Grid System(DGGS)is a type of spatial reference system that tessellates the globe into many individual,evenly spaced,and well-aligned cells to encode location and,thus,can serve as a basis for data cube construction.This facilitates integration and aggregation of multi-resolution data from various sources to rapidly calculate spatial statistics.We calculated normalized area and compactness for cell geometries from 5 open-source DGGS implementations-Uber H3,Google S2,RiskAware OpenEAGGR,rHEALPix by Landcare Research New Zealand,and DGGRID by Southern Oregon University-to evaluate their suitability for a global-level statistical data cube.We conclude that the rHEALPix and OpenEAGGR and DGGRID ISEA-based DGGS definitions are most suitable for global statistics because they have the strongest guarantee of equal area preservation-where each cell covers almost exactly the same area on the globe.Uber H3 has the smallest shape distortions,but Uber H3 and Google S2 have the largest variations in cell area.However,they provide more mature software library functionalities.DGGRID provides excellent functionality to construct grids with desired geometric properties but as the only implementation does not provide functions for traversal and navigation within a grid after its construction.