Orbit Determination Research Articles

Research on Inter-Satellite Laser Ranging Scale Factor Estimation Methods for Next-Generation Gravity Satellites

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations.

Message from the Guest Editors of the Special Issue on Precise Orbit Determination

Message from the Guest Editors of the Special Issue on Precise Orbit Determination

Antenna and attitude modeling of modernized GLONASS satellites

Next to the legacy frequency division multiple access (FDMA) signals in the L1 and L2 band, modernized GLONASS satellites of the M+, K1, and K2 generation also transmit new code division multiple access (CDMA) signals on L3, and, in part, the L1 and L2 frequencies. Depending on the specific satellite platform, either a common antenna or two distinct antennas are used for the individual signals. As a novel feature, the new CDMA navigation messages provide information on the antenna phase center locations as well as the spacecraft orientation during rate-limited noon and midnight turns. We establish a comprehensive set of phase center positions for the individual GLONASS antennas from manufacturer data and information in the CDMA navigation messages, inferred from the comparison of FDMA and CDMA broadcast ephemerides, and obtained from antenna baseline estimates using a triple-frequency carrier phase combination. Based on these, reference values for the signal-specific PCOs of each block of modernized GLONASS spacecraft are derived that may be used to extend the current antenna model of the International GNSS Service (IGS) to all frequency bands. Complementary to the analysis of antenna phase center information, the new CDMA attitude model for GLONASS-K satellites is reviewed. Algorithms for computing relevant parameters of the rate-limited yaw slews including the ramp-up and -down phase based on the Sun/orbit geometry are derived that enable a concise attitude modeling in GLONASS orbit determination and precise point positioning. The model is validated through comparison with yaw angle estimates derived from triple-frequency observations showing consistency at the 1° level for the K2 satellite. On the other hand, unexpected accelerations during noon turns of GLONASS-M+ are identified, which may cause short-term yaw angle deviations of up to 20° relative to attitude models in common use within the IGS.

Precise orbit determination for Tianwen-1 during mapping phase

Precise orbit determination for Tianwen-1 during mapping phase

Analysis and comparison of the orbit determination accuracy of TianQin based on multiple ground-based measurements

TianQin project, a Chinese initiative in space gravitational wave detection, demands high precision in satellite orbit during both entry and scientific operations. As means of developmental maturation, ground-based measurements play a vital role in ensuring the smooth execution of TianQin satellite’s detection mission. This paper conducts a simulation analysis by utilizing various ground-based measurement data, including the China Deep Space Network (CDSN), S/Ka-band ranging system, and Satellite Laser Ranging (SLR). The main focus is to explore the distinctions in Precise Orbit Determination (POD) capabilities among different methods and to enhance POD accuracy through the integration of multiple techniques for TianQin satellites. The results indicate: (1) Leveraging a strategically positioned station distribution, CDSN stations offer extended observation time, averaging 17.3 h per satellite daily, compared to S/Ka’s 10.5 h. (2) In single-measurement POD scenarios, S/Ka proves superior, achieving accuracy better than 10 m and 0.4 mm s−1 for TianQin satellites with a 7-day orbit arc length. This superiority is attributed to its exceptional observational accuracy, outperforming CDSN’s 40 m and 2.2 mm s−1 for POD accuracy. (3) By integrating high-precision SLR data on the foundation of CDSN or S/Ka observations, the POD accuracy of TianQin satellites is further enhanced, despite the limited SLR data quantity.

Contribution of landmark-tracking data to the estimation of the gravity field and rotation parameters of 311P/PANSTARRS for the incoming Tianwen-2 space mission

311P/PANSTARRS is one of the two targets of the Chinese asteroid exploration mission Tianwen-II. The estimation of the gravity field and rotation parameters is an important part of the mission. Optical landmark observations directly record the relative relationship between the asteroid and probe. For this purpose, we investigate the role of the addition of landmark observations to radio-tracking data in achieving precise orbit determination and deriving the physical parameters of 311P. More specifically, we use a linear re-weighting fusion scheme to aggregate these two heterogeneous data to determine 311P's gravitational field and rotational parameters. Our results show that landmark observations enhance parameter estimation drastically. We conduct extensive experiments to understand how to optimize the use of landmark observations. Besides, we find that the upper bound error on 311P ephemeris for estimating a 2nd-degree gravity field model is 5 km.

Orbit determination from one position vector and a very short arc of optical observations

In this paper, we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1$$\\end{document} and a very short arc (VSA) of optical observations A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}_2$$\\end{document}. Using the conservation laws of the two-body dynamics, we write the problem as a system of 8 polynomial equations in 6 unknowns. We prove that this system is generically consistent, namely, for a generic choice of the data P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document}, it always admits solutions in the complex field, even when P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document} do not correspond to the same celestial body. The consistency of the system is shown by deriving a univariate polynomial v\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {v}$$\\end{document} of degree 8 in the unknown topocentric distance at the mean epoch of the observations of the VSA. Through Gröbner bases theory, we also show that the degree of v\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {v}$$\\end{document} is minimum among the degrees of all the univariate polynomials solving this problem. Even though we can find solutions to our problem for a generic choice of P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document}, most of these solutions are meaningless. In fact, acceptable solutions must be real and have to fulfill other constraints, including compatibility with Keplerian dynamics. We also propose a way to select or discard solutions taking into account the uncertainty in the data, if present. The proposed orbit determination method is relevant for different purposes, e.g., the computation of a preliminary orbit of an Earth satellite with radar and optical observations, the detection of maneuvres of an Earth satellite, and the recovery of asteroids which are lost due to a planetary close encounter. We conclude by showing some numerical tests in the case of asteroids undergoing a close encounter with the Earth.

Precise Orbit Determination for Maneuvering HY2D Using Onboard GNSS Data

The Haiyang-2D (HY2D) satellite is the fourth ocean dynamics environment monitoring satellite launched by China. The satellite operates on a re-entry frozen orbit, which necessitates orbital maneuvers to maintain its designated path once the satellite’s sub-satellite point deviates beyond a certain threshold. However, the execution of orbit maneuvers presents a significant challenge to the field of Precise Orbit Determination (POD). The thesis selects the on-board GPS data of HY2D satellite in December 2023 and five maneuvering days of that year. Employing a multifaceted approach that includes the assessment of observational data quality, orbit overlap, external orbit validation, and SLR (Satellite Laser Ranging) verification, the research delves into precise orbit determination during both maneuver and non-maneuver periods. The results indicate that: (1) The average number of satellites tracked by the receiver is 6.4; (2) During the non-maneuver periods, the average RMS (Root Mean Square) value of the radial difference in the 6-h overlapping arc segment is 0.66 cm, and the three-dimensional position difference is about 1.16 cm; (3) When compared with the precision science orbits (PSO) provided by CNES (Centre National d’Études Spatiales), the average values of the RMS values of the differences in the radial (R), transverse (T), and normal (N) directions during the non-maneuver and maneuver periods are respectively 1.32 cm, 2.31 cm, 1.92 cm and 3.04 cm, 8.78 cm, 2.72 cm. (4) The SLR verification of the orbit revealed a residual RMS of 2.24 cm. This suggests that by incorporating the modeling of maneuver forces during the maneuver periods, the impact of orbital maneuvers on orbit determination can be mitigated.

Extension of the BDS IGSO and MEO satellite antenna patterns with FengYun-3C and LuTan-1 onboard data

The International Global Navigation Satellite System (GNSS) Service (IGS) has recommended calibrating the extended satellite antenna Phase Center Variation (PCV) model for all navigation satellites to support low-Earth-Orbit (LEO) satellite applications. Owing to the absence of ground-calibrated PCVs for the BeiDou Navigation Satellite System (BDS), tracking data from global ground stations were used for in-orbit estimations. However, limited by the observed maximum nadir angle, PCVs based on ground data cannot cover the entire range of nadir angles observed using by LEO satellites. In this study, the FengYun-3C and LuTan-1 missions were used to extend the PCVs of the BDS Inclined GeoSynchronous orbit (IGSO) and medium-Earth-orbit (MEO) satellites. The PCVs corresponding to the ionosphere-free linear combinations of B1I/B2I, B1I/B3I, and B1C/B2a were calibrated in-orbit by extending the maximum nadir angle from 9° to 10° for the IGSO and from 13° to 15° for the MEO. There was good consistency among the estimated PCVs of satellites of the same type. In addition, these estimated PCVs were close to the corresponding satellite block-specific values estimated based on ground tracking data. The impact of the extended PCVs of the BDS satellite antenna was investigated by comparing them with the unextended PCVs model in the receiver antenna PCVs pattern estimation and precise orbit determination of the FengYun-3C and LuTan-1 satellites. The results showed that the extended BDS satellite PCVs effectively reduced the unmodeled error of the unextended BDS satellite PCVs in the low-elevation region of the LEO receiver antenna PCV patterns. In addition, compared with the introduction of phase center offset alone, the introduction of ground-based PCVs can improve the overlapping orbit differences (OODs) of LEO satellites, and the extended BDS satellite PCVs can further improve the OODs. Taking B1C/B2a as an example, the improvement ratio of OODs in the 3D direction of Lutan-1A increased from 5.2 % to 8.0 %, and that of Lutan-1B can rise from 1.7 % to 4.2 %.

Robust UKF orbit determination method with time-varying forgetting factor for angle/range-based integrated navigation system

The angle/range-based integrated navigation system is a favorable navigation solution for deep space explorers. However, the statistical characteristics of the measurement noise are time-varying, leading to inaccuracies in the derived measurement covariance even causing filter divergence. To reduce the gap between theoretical and actual covariances, some adaptive methods use empirically determined and unchanged forgetting factors to scale innovations within the sliding window. However, the constant weighting sequence cannot accurately adapt to the time-varying measurement noise in dynamic processes. Therefore, this paper proposes an Adaptive Robust Unscented Kalman Filter with Time-varying forgetting factors (TFF-ARUKF) for the angle/range integrated navigation system. Firstly, based on a statistically linear regression model approximating the nonlinear measurement model, the M-estimator is adopted to suppress the interference of outliers. Secondly, the covariance matching method is combined with the Huber linear regression problem to adaptively adjust the measurement noise covariance used in the M-estimation. Thirdly, to capture the time-varying characteristics of the measurement noise in each estimation, a new time-varying forgetting factors selection strategy is designed to dynamically adjust the adaptive matrix used in the covariance matching method. Simulations and experimental analysis compared with EKF, AMUKF, ARUKF, and Student’s t-based methods have validated the effectiveness and robustness of the proposed algorithm.

Pulsed Laser Links Simulation for Small Satellite Clock Model Estimation

The expansion of satellite constellation applications brings attention to the need for responsive, reliable satellite communication. For preflight technology assessment of missions, a simulation of two spacecraft in low Earth orbit has been created to estimate clock synchronization and precision orbit determination based on measured instrumentation performance. A novel MATLAB-based numerical simulator was developed to model spacecraft-to-spacecraft laser time-transfer and estimate the offset between the spacecraft clocks over time. This simulation includes timing errors associated with laser pulse detection, as well as non-Gaussian clock drift models. Two on-board clocks are modeled: a cesium-based chip-scale atomic clock and a rubidium-based miniature atomic clock. The positions and velocities of the spacecraft at a reference epoch and the constant coefficients of a polynomial clock model are estimated. Results compare the estimated clock model of a mission operation that only uses GPS measurements and one that uses both GPS and laser pulse time-of-flight measurements between spacecraft referenced to their on-board clocks. Including lasing measurements reduces the root-mean-square clock model error to approximately 80% of the RMS of the cases with only GPS measurements. This simulation tool can be used to optimize the lasing operations schedule based on mission timing performance objectives.

Neural Network–Assisted Initial Orbit Determination Method for Libration Point Orbits

Neural Network–Assisted Initial Orbit Determination Method for Libration Point Orbits

Precise point positioning (PPP) based on the machine learning-based ionospheric tomography

Undifferenced and Uncombined Precise Point Positioning (UPPP) currently stands as a prominent research area, where the integration of high-precision ionospheric products holds the potential to substantially enhance accuracy and convergence performance in UPPP. Presently, the majority of external ionospheric constraints for UPPP rely on Global Ionospheric Maps (GIM). However, the accuracy and resolution of GIM fall short, imposing significant limitations on the positioning performance of UPPP. Consequently, this paper introduces the application of Computerized Ionospheric Tomography based on Machine Learning (CIT-ML) to enhance UPPP performance (PPP-CIT-ML). In this approach, we convert the three-dimensional electron density of CIT-ML into vertical total electron content (VTEC), and then it is compiled into ionospheric grid files essential for UPPP. Simultaneously, the traditional ionospheric tomography methods based on the improved algebraic reconstruction technique (IART) is also employed for UPPP (PPP-CIT-IART), alongside the ionospheric grid files broadcasted by the Center for Orbit Determination in Europe (CODE) for UPPP (PPP-CODE), where PPP-CIT-IART and PPP-CODE are used as the reference methods to test the performance of PPP-CIT-ML. In Static and Kinematic UPPP, compared to PPP-CODE, PPP-CIT-IART demonstrated average improvements in positioning accuracy and convergence performance by over 10% and 7%, respectively. PPP-CIT-ML showed average improvements in positioning accuracy and convergence performance by over 26% and 28%, respectively. The extrapolated ionospheric electron density (IED) applied to UPPP (ECIT-ML-PPP) and compared with PPP-CODE displayed average improvements in positioning accuracy by over 21% and convergence performance by over 26%. Compared with PPP-CIT-IART, ECIT-ML-PPP displayed average improvements in positioning accuracy and convergence performance by over 6% and 21%, respectively. These findings highlight that ionospheric error correction information obtained through ionospheric tomography significantly enhances the positioning accuracy and convergence performance of UPPP. Moreover, the performance enhancement achieved through machine learning-based ionospheric tomography is more pronounced. This study provides preliminary validation for the feasibility of applying machine learning-based ionospheric tomography results to navigation positioning.

Joint analysis of JUICE and Europa Clipper tracking data to study the Jovian system ephemerides and dissipative parameters

Context. Jupiter and its moons form a complex dynamical system that includes several coupling dynamics at different frequencies. In particular the Laplace resonance is fundamental to maintaining the energy dissipation that sustain Io’s volcanic activity and Europa’s subsurface ocean; studying its stability is thus crucial for characterizing the potential habitability of these moons. The origin and evolution of the Laplace resonance is driven by the strong tidal interactions between Jupiter and its Galilean moons, and the future planetary exploration missions JUICE and Europa Clipper could bring new light to this unsolved mechanism. During the Jupiter tours of both missions and JUICE’s Ganymede orbital phase, two-way radiometric range and Doppler data will be acquired between Earth ground stations and the spacecraft, which will be processed to recover the static and time-varying gravity field of the moons. Moreover, range and Doppler data will improve the orbit accuracy of the moons, providing precise measurements of Jupiter’s tidal parameters. Aims. This work presents a covariance analysis of the joint orbit determination of JUICE and Europa Clipper, aimed at quantifying the expected uncertainties on the main parameters that characterize the dynamics of the Jupiter system. Methods. We simulated radio science data from JUICE and Clipper missions under conservative noise assumptions, using a multi-arc approach to estimate the ephemerides and dissipation in the system. Results. Even though JUICE and Europa Clipper will not perform flybys of Io, the strong coupling with Europa and Ganymede will allow an improvement of our knowledge of the Jupiter-Io dissipation parameters thanks to JUICE and Europa Clipper radiometric data. Moreover, the expected uncertainty in Jupiter’s dissipation at the frequency of Callisto could unveil a potential resonance locking mechanism between Jupiter and Callisto.

Satellite orbit determination and time synchronization using GPS single-frequency observables in low and high solar activities

We assess the orbit accuracy and time synchronization error using the L1 and C1 observables during the different solar activities. In general, GPS single-frequency (SF) observable can be used for commercial applications in satellite industry. The accuracy of satellite orbit determination using the SF observations is dominated by solar activities. The solar activities are indexed by the F10.7 value. The different solar activities lead to the ionosphere perturbation, triggering off the occurrence probability of ionospheric irregularities. The ionospheric irregularity affects the amplitude and phase of GPS signal. The affected amplitude and phase are indexed by the S4 value. We determine the GRACE satellite orbit using the SF GPS observations and compare the resulting orbit to that derived by dual-frequency observations for the effectiveness. The SF phase data are very sensitive to the variation in electron density and indirectly affects both the orbit accuracy and the time synchronization error. This is most likely caused by the phase ambiguity disturbed by the ionosphere. However, the C1 is relatively free from such a disturbance due to the strong signal-to-noise ratio (SNR) and the phase shift keying technique. The C1 performs the consistent solution over the low and high solar activities. However, this is not the case for the L1. The L1-derived orbit solution during the high solar activities is worse than that during the low solar activities. On the other hand, the time synchronization errors derived by the L1 and C1 are also different. The L1-derived time synchronization error has a relatively large perturbation as compared to the C1-derived one, which shows a consistent solution for a long-term period. This work suggests that the C1 observable is able to produce a consistent the orbit solution and time synchronization for the commercial applications of the satellite industry.Graphical

Overview on Space-Based Optical Orbit Determination Method Employed for Space Situational Awareness: From Theory to Application

Overview on Space-Based Optical Orbit Determination Method Employed for Space Situational Awareness: From Theory to Application

Space interferometer orbit determination with multi-GNSS

Spacecraft positioning plays a crucial role in scientific space mission design, as well as in the further scheduling of scientific observations for such a mission. We examine the application of global navigation satellite systems (GNSS) to solve the orbit determination problem in a pure space very long baseline interferometer (VLBI) project. A network of GPS, GLONASS, Galileo and BeiDou navigation satellites may be a more efficient solution to determining the position and velocity of space radio telescopes and space interferometer baselines. For such a project, it is necessary to take into account the special conditions of GNSS observations, as well as the high accuracy of determining not only position but also velocity. In this paper, we estimate visibility of navigation satellite systems for Low and Medium orbits of a pure space-VLBI system and simulate GNSS code and phase measurements. Orbit determination was performed on smoothed code measurements. Phase measurements simulated with a step of 1 s and combined in Doppler measurements yield average position and velocity errors of 1.01 m and 8.8 mm/s in Medium Earth orbit. The results showed that GNSS observations are sufficient to solve the problems of orbit determination of a space-VLBI interferometer both in Low-Earth and Medium Earth orbits.

Precise orbit determination of the LuTan satellite using GPS, BDS-2, and BDS-3 signals

Abstract The LuTan satellite is the first formation-flying mission of China enabling synthetic aperture radar interferometry in the L-band. As a key mission requirement, the absolute position of each satellite must be determined with an accuracy of 5 cm in three dimensions (3D). To fulfill this demand, each satellite carries a Global Positioning System/Beidou Navigation Satellite System (GPS/BDS) dual-constellation Global Navigation Satellite System receiver that can simultaneously track the GPS L1 and L2 signals, the BDS-2 B1I and B3I signals (BD2), and the BDS-3 B1C and B2a signals (BD3). In this study, we assess the performances of precise orbit determination with different signals and their combinations. For that purpose, we produce a total of five sets of orbit solutions, i.e., GPS-based, BD2-based, BD3-based, GPS/BD2 combined, and GPS/BD3 combined solutions. To evaluate the orbit solutions, comparisons in the orbital overlaps and with the GPS-based orbit are adopted. The orbital overlap analysis shows that the GPS-based solution has the smallest root mean square (RMS) of overlap orbit differences than other single-constellation solutions with 3.7 mm in 3D. The BD2- and BD3-based orbits are suffered from large errors and the overlap RMS differences are 24.7 and 18.9 mm, respectively. Furthermore, all of the combined orbits (both 3.1 mm for the GPS/BD2 and GPS/BD3 combined orbits) based on the variance component estimation method can obtain improvement than GPS-based solutions. For orbit comparisons, the GPS-based solution is selected to serve as the reference. The RMS values of the orbit differences are 29.9 and 15.4 mm for the BD2- and BD3-based solutions, respectively. For the GPS/BD2 and GPS/BD3 combined solutions, the values are 4.1 and 4.8 mm. In general, the results agree with those obtained in the overlap analysis. These results indicate that the BD3-based orbit is superior to the BD2-based orbit, while both of them are inferior to the GPS-based orbit. We show that inaccurate ephemerides of the BDS satellites can partly explain the degraded performance of the BDS-derived orbits. Nevertheless, the orbits still fulfill the 5 cm accuracy demand and can be readily used for subsequent precise baseline determination.

Telescopic Network of Zhulong for Orbit Determination and Prediction of Space Objects

The increasing proliferation of space debris, intermittent space incidents, and the rapid emergence of massive LEO satellite constellations pose significant threats to satellites in orbit. Ground-based optical observations play a crucial role in space surveillance and space situational awareness (SSA). The Zhulong telescopic observation network stands as a pivotal resource in the realm of space object tracking and prediction. This publicly available network plays a critical role in furnishing essential data for accurately delineating and forecasting the orbit of space objects in Earth orbit. Comprising a sophisticated array of hardware components including precise telescopes, optical sensors, and image sensors, the Zhulong network synergistically collaborates to achieve unparalleled levels of precision in tracking and observing space objects. Central to the network’s efficacy is its ability to extract positional information, referred to as angular data, from consecutive images. These angular data serve as the cornerstone for precise orbit determination and prediction. In this study, the CPF (Consolidated Prediction Format) orbit serves as the reference standard against which the accuracy of the angular data is evaluated. The findings reveal that the angular data error of the Zhulong network remains consistently below 3 arcseconds, attesting to its remarkable precision. Moreover, through the accumulation of angular data over time, coupled with the utilization of numerical integration and least squares methods, the Zhulong network facilitates highly accurate orbit determination and prediction for space objects. These methodologies leverage the wealth of data collected by the network to extrapolate trajectories with unprecedented accuracy, offering invaluable insights into the behavior and movement of celestial bodies. The results presented herein underscore the immense potential of electric optic telescopes in the realm of space surveillance. By harnessing the capabilities of the Zhulong network, researchers and astronomers can gain deeper insights into the dynamics of space objects, thereby advancing our understanding of the cosmos. Ultimately, the Zhulong telescopic observation network emerges as a pioneering tool in the quest to unravel the mysteries of the universe.

Mass, Density, and Radius of Asteroid (16) Psyche from High-precision Astrometry

We characterize asteroid (16) Psyche using high-precision astrometry, including the recent Gaia Focused Product Release. The gravitational perturbations of Psyche on other asteroids can be observable in the case of mutual encounters. Using a least squares approach, we estimate the mass of Psyche by fitting astrometric data of asteroids that come within 0.05 au of Psyche. Combining the resulting individual estimates, we find GM = 1.601 ± 0.017 km3 s−2. This result is robust against variations in the orbit determination setup and specific data set used. The volume and equivalent radius of Psyche are currently constrained by occultations and radar and optical imaging to (5.75 ± 0.19) × 106 km3 and 111−0.5+2 km, respectively. Given the volume of Psyche, our mass estimate corresponds to a bulk density of 4172 ± 145 kg m−3, which is compatible with an M-type taxonomic classification. Finally, the phase-dependent photocenter offset is visible in the residuals of Gaia astrometric observations of Psyche. This effect is consistent with the size of Psyche.