We developed llrtoolkit(https://www.llrtoolkit.online), a high-precision platform designed for the comprehensive processing of lunar laser ranging (LLR) data from both global and domestic stations. Beyond standard data reduction, the platform supports the generation of Consolidated Prediction Format (CPF) products for lunar surface retroreflectors and cislunar space satellites. The development of this platform is motivated by the expanding network of Chinese LLR stations and the rapid accumulation of observational data, addressing the processing delays in existing international services and their lack of support for cislunar space satellites and newly deployed retroreflectors (e.g., NGLR-1). By incorporating multi-threaded parallel computing, the llrtoolkit platform significantly enhances computational efficiency, increasing the processing throughput from 20 to 130 records per second. Initial validation using recent LLR observations demonstrates that the root mean square (RMS) of two-way range residuals (O–C) consistently reaches the centimeter level. The generated CPF products have been successfully implemented in LLR experiments and provided essential support for China's first lunar-distance satellite laser ranging, confirming the platform’s practical utility for high-precision lunar and cislunar missions.

China launched its first Mars mission in 2020 and is scheduling a sample return mission in 2028. Such deep space missions require high-precision Earth-Mars radio tracking. However, Corotating Interaction Regions (CIRs) in the solar wind can pose considerable influence on the radio link. This study constructs a CIR density model embedded within a quiescent solar wind background, assuming a solar rotation period of 26 days. We integrate the plasma density along the line-of-sight over two three-year spans (2020.07-2023.07 and 2029.01-2032.01) to simulate periodic CIR crossings. Results indicate that CIR-induced Total Electron Content (TEC) enhancements fluctuate between 40 TECU at Mars opposition and 330 TECU, a pattern primarily dictated by the 26 month planetary synodic cycle. The most significant link impairments are projected for 2021 January-July and 2029 June-2030 February, periods which conversely offer optimal geometries for radio sounding of CIR structures. Given that multiple CIRs may intersect the ray path simultaneously, their cumulative delays must be integrated into future navigation models to safeguard mission accuracy.

The realization of clock synchronization and syntonization via inter-satellite link is of vital importance for navigation, space-based Very Long Baseline Interferometry (VLBI) experiments and precision tests of fundamental physics. We study the accuracy and stability of time and frequency transfer via inter-satellite link in Cis-lunar space. A relativistic time transfer model using microwave dual one-way ranging (DOWR) is developed. Taking the distant retrograde orbit (DRO)-low Earth orbit (LEO) inter-satellite link as an instance, sub-nanoseconds level accuracy is achieved. We analyze the error in orbit determination of LEO satellite and DRO satellite. With the models of relative velocity correction, relativistic frequency shift and Shapiro delay, the stability of time transfer is studied. The result shows the DOWR microwave link would support clock synchronization with a time stability of better than 14.3 ps over 1000 s, better than 100.5 ps over one day, with the accuracy constraints on the orbit determination of the LEO satellite 10 cm and DRO satellite 50 m in position. If the longer time stability of hardware delay reaches ps level, the performance of DOWR time transfer link can be further improved to support the distribution of the time-frequency scale established by an active hydrogen maser with a frequency stability of 2x10-15 over one day. We estimated that high-performance DRO-LEO time and frequency comparisons may support the gravitational redshift tests at a 10-6 level and the space-based VLBI experiments to improve the orbit determination of deep-space probes by one to two orders of magnitude.

China is planning to launch the “Tianwen-4” mission around the year 2030, with its aim being the exploration of Jupiter and its moon, Callisto. Within the realm of deep space exploration, the accuracy of ephemerides is of great importance. Current ephemerides employ a simplified rotation model for Callisto, which this study addresses by proposing a novel dynamical model. This model enhances the existing orbital dynamics by integrating Callisto’s rotational motions influenced by gravitational torques from the Sun, Jupiter, and other Galilean moons within an inertial frame, capturing the intricate coupling between Callisto’s orbital and rotational dynamics. The study establishes a full dynamical model by deriving analytical expressions for this coupling and developing an adjustment model for data fitting using precise orbit determination methods. Furthermore, the influence of tidal effects on Callisto’s motion is investigated, considering its multilayered internal structure. Results demonstrate that the difference between the newly established full model and the model in current ephemerides is on the order of tens of meters. When calculating the impact of different internal structures of Callisto on its orbit, the influence of three-layered and two-layered structures is on the order of meters, suggesting that the development of a high-precision dynamical model requires additional constraints on the internal structure of Callisto. This research provides a novel alternative for a new generation of precise numerical ephemerides for Callisto. Additionally, these findings provide a testing platform for the data from the “Tianwen-4” mission.

This paper provides a comprehensive overview of the development of Lunar Laser Ranging (LLR), covering key components such as ground observatories, lunar retro-reflectors, and data formats. The paper details the evolution of LLR experiments conducted by some major world-class observatories, with a particular focus on addressing critical issues associated with LLR technology. Additionally, the article highlights the latest advancements in the field, elucidating scientific achievements derived from LLR data, including its contributions to gravitational theory, Earth Orientation Parameters, lunar physics exploration, and lunar librations. The review summarizes new challenges in LLR modeling and concludes with prospects for the future development of LLR.

China will launch the “Tianwen-IV” mission around 2030, focusing on the orbiting exploration of Jupiter and Callisto, a moon of Jupiter. As part of this ambitious mission, a main satellite will carry another satellite that will be released in the Jupiter system to continue its journey toward Uranus. Considering the current mission planning, we propose an inter-satellite radio-observation mode that differs from the conventional observation mode of tracking from Earth to precisely determine the orbit of the satellites. Given the significance of the Callisto gravity field model in both science objectives and satellite navigation, we have conducted a series of simulation experiments to evaluate the potential of this inter-satellite range-rate data for accurately estimating the Callisto gravity field. The results obtained from the analysis demonstrate that by utilizing 40 days of ground station observations, it is possible to estimate the gravity field model of Callisto up to a degree of 70. Remarkably, when combining these ground station observations with inter-satellite observations, a comparable level of accuracy can be achieved with just 10 days of observations. Furthermore, with reduced inter-satellite observation noise, accuracy improves, enabling estimation up to 80 degrees or higher. Initial inter-satellite distance selection impacts estimation accuracy. These findings serve as a valuable test bed for the future “Tianwen-IV” mission to perform precise orbit determination and gravity field model estimation to reduce reliance on deep space stations.

Context . High-precision ephemerides are not only useful in supporting space missions, but also in investigating the physical nature of celestial bodies. This paper reports an update to the orbit and rotation model of the Martian moon Phobos. In contrast to earlier numerical models, this paper details a dynamical model that fully considers the rotation of Phobos. Here, Phobos’ rotation is first described by Euler’s rotational equations and integrated simultaneously with the orbital motion equations. We discuss this dynamical model, along with the differences with respect to the model now in use. Aims . This work is aimed at updating the physical model embedded in the ephemerides of Martian moons, considering improvements offered by exploiting high-precision observations expected from future missions (e.g., Japanese Martian Moons exploration, MMX), which fully supports future studies of the Martian moons. Methods . The rotational motion of Phobos can be expressed by Euler’s rotational equations and integrated in parallel with the equations of the orbital motion of Phobos around Mars. In order to investigate the differences between the two models, we first reproduced and simulated the dynamical model that is now used in the ephemerides, but based on our own parameters. We then fit the model to the newest Phobos ephemeris published by Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE). Based on our derived variational equations, the influence of the gravity field, the Love number, k 2 , and the rotation behavior were studied by fitting the full model to the simulated simple model. Our revised dynamic model for Phobos was constructed as a general method that can be extended with appropriate corrections (mainly rotation) to systems other than Phobos, such as the Saturn and Jupiter systems. Results . We present the variational equation for Phobos’ rotation employing the symbolic Maple computation software. The adjustment test simulations confirm the latitude libration of Phobos, suggesting gravity field coefficients obtained using a shape model and homogeneous density hypothesis should be re-examined in the future in the context of dynamics. Furthermore, the simulations with different k 2 values indicate that it is difficult to determine k 2 efficiently using the current data.

This paper introduces a novel dynamical model, building upon the existing dynamical model for Deimos in the current numerical ephemerides, which only encompasses the simple libration effects of Deimos. The study comprehensively incorporates the rotational dynamics of Deimos influenced by the torque exerted by the major celestial bodies (Mars, the Sun) in the solar system within the inertial space. Consequently, a full dynamical model is formulated to account for the complete coupling between the rotation and orbit of Deimos. Simultaneously, employing precision orbit determination methods used for artificial satellites, we develop an adjustment model for fitting data to the complete model. The 12-order Adams–Bashforth–Moulton (ABM) integration algorithm is employed to synchronously integrate the 12 state variables of the full model to obtain the orbit of Deimos.The difference in the orbits obtained by integrating the full model over a period of 10 years and those obtained by the simplified model is at the order of 10 km. After precise orbit determination, this difference decreases to below 100 m, so numerical simulation results indicate that the full dynamical model and adjustment model are stable and reliable. Simultaneously, the integration of the Deimos third-order gravity field in the full model over a 10-year period induces only meter-level positional changes. This suggests that when constructing the complete model, the utilization of a second-order gravity field alone is sufficient. Compared to the simple model, the polar axis of Deimos in the inertial space exhibits a more complex oscillation in the full model. Additionally, the full model calculates that the minimum moment of inertia principal axis of Phobos has an amplitude of approximately 0.5 degrees in the longitude direction and does not exceed 2 degrees in the latitude direction. This work further advances the current dynamical model for Deimos and establishes the foundational model for the generation of a new set of precise numerical ephemerides for Deimos.

This paper provides a comprehensive overview of the development of Lunar Laser Ranging(LLR),covering key components such as ground observatories,lunar retro-reflectors,and data formats.The paper details the evolution of LLR experiments conducted by some major world-class observatories,with a particular focus on addressing critical issues associated with LLR technology.Additionally,the article highlights the latest advancements in the field,elucidating scientific achievements derived from LLR data,including its contributions to gravitational theory,Earth Orientation Parameters,lunar physics exploration,and lunar librations.The review summarizes new challenges in LLR modeling and concludes with prospects for the future development of LLR.

High-precision ephemerides not only support space missions,but can also be used to study the origin and future of celestial bodies.In this paper,a coupled orbit-rotation dynamics model that fully takes into account the rotation of the Martian moons is developed.Phobos and Deimos’rotations are first described by Eulerian rotational equations,and integrated simultaneously with the orbital motion equations.Orbital and orientational parameters of Mars satellites were simultaneously obtained by numerical integration for the first time.In order to compare the differences between our newly developed model and the one now used in the ephemerides,we first reproduced and simulated the current model using our own parameters,and then fit it to the Institut de Mécanique Céleste et de Calcul deséphémérides ephemerides using least-square procedures.The adjustment test simulations show Phobos and Deimos’orbital differences between the refined model and the current model are no more than 300 m and125 m,respectively.The orientation parameters are confirmed and the results are in good agreement with the International Astronomical Union results.Moreover,we simulated two perturbations (main asteroids and mutual torques) which were not included in our refined model,and find that their effects on the orbits are completely negligible.As for the effect on rotation,we propose to take care of the role of mutual attraction in future models.

An accurate gravity field model of Deimos can provide constraints for its internal structure modeling, and offer evidence for explaining scientific issues such as the origin of Mars and its moons, and the evolution of the Solar System. The Japanese Martian Moon Exploration (MMX) mission will be launched in the coming years, with a plan to reach Martian orbit after 1 year. However, there is a lack of executed missions targeting Deimos and research on high-precision gravity field of Deimos at this stage. In this study, a 20th-degree gravity field model of Deimos was constructed by scaling the gravity field coefficients of Phobos and combining them with an existing low-degree gravity field model of Deimos. Using simulated ground tracking data generated by three stations of the Chinese Deep Space Network, we simulate precise tracking of a spacecraft in both flyby and orbiting scenarios around Deimos, and the gravity field coefficients of Deimos have been concurrently computed. Comparative experiments have been conducted to explore factors affecting the solution, indicating that the spacecraft’s orbital altitude, the noise level of observation data, and the ephemeris error of Deimos have a significant impact on the solution results. The results of this study can provide references for planning and implementation of missions targeting Martian moons.

This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, when the laser ranging pulse width is 10 picoseconds or less, it is possible to distinguish from which specific corner cubes within the CCR array each peak in the echo signal originates. Consequently, partial data from the echo can be extracted for signal processing, significantly reducing random errors and improving the single-shot precision of LLR. The distance obtained by extracting part of the echo can be reduced to the center position of the array, thereby providing multiple higher-precision ranging results from each measurement. This not only improves the precision of LLR but also increases the data volume. A simulation experiment based on the 1.2 m laser ranging system at Yunnan Observatories was conducted. By extracting one peak for signal processing, the single-shot precision improved from 32.24 mm to 2.52 mm, validating the theoretical analysis results. Finally, an experimental laser ranging system based on a 53 cm binocular telescope system was established for ground experiments. The experimental results indicated that the echo signal could identify the tilt state of the CCR array. By extracting the peak returned by the central CCR for signal processing, the ranging precision was greatly improved. Through theoretical analyses, simulation experiments, and ground experiments, a solution to reduce the random errors caused by the tilt of the CCR array was provided. This offers an approach to enhance the single-shot precision of future LLR and provides a reference for upgrading ground-based equipment at future laser ranging stations.

Space Debris Laser Ranging (DLR) is a technique to measure range to defunct satellites, rocket bodies or other space targets in orbits around Earth. The analysis shows that one of the reasons for the low success probability of DLR is the inaccurate orbital prediction of targets. Then it is proposed to use the Superconducting Nanowire Single-Photon Detector (SNSPD) running in automatic-recoverable range-gate-free mode, in which case, the effect of the accuracy of the target’s orbital prediction on the success probability of DLR is greatly reduced. In this way, 249 space debris were successfully detected and 532 passes of data were obtained. The smallest target detected was the space-debris (902) with an orbital altitude of about 1000 km and a Radar Cross Section (RCS) of 0.0446 m 2 . The farthest target detected was the space-debris (12,445) with a large elliptical orbit and an RCS of 18.2505 m 2 , of which the range of the normal point (NPT) of the measured arc-segment on January 27, 2019 was 6260.805 km.

为发展月球和行星探测,美国喷气推进实验室(Jet Propulsion Laboratory,JPL)、法国天体力学与历算研究所(Institut de Mécanique Céleste et de Calcul deséphémérides,IMCCE)、俄罗斯科学院应用天文研究所(Institute of Ap-plied Astronomy of the Russian Academy of Sciences,IAA RAS)分别研制了各自的行星历表.就各个行星历表的发展历程进行概括,对最新版本的3个历表DE438、INPOP19a和EPM2017进行分析,并通过仿真计算比较了月球和行星在太阳质心参考系中的位置和速度的差异,评估了最新历表的相对精度,为中国深空探测和自主历表研制提供技术支撑.结果表明,历表间差异均较小,但月球历表的精度有待提高.

Lunar laser ranging (1.I,R) has promoted the development of earth-moon science, lunar spatial reference, and gravitational physics. To fully use the LLR data according to the widely used International Earth Rotation Service 2010 (IERS 2010) specification, the solid tide, ocean tide, atmospheric delay, and general relativity effects are modeled, and the 1.I,R observation model is established in this paper. All 1.1.R observation data provided by the International Laser Ranging Service are checked with the model, and the generated Lunar Corner Reflector Prediction File in CPF (Consolidated prediction format) supports Yunnan Observatory's independent 1,1,R observations. The INPOP19a, DE430, and EPM2017 almanacs are input as observation models to check the LLR standard point data. The results show that the INPOP19a almanac is closest to the measured data than other almanacs.

In this article, we study the orbital dynamics with the gravitational potential of the asteroid 93 Minerva using an irregular shape model from observations. We calculate its physical size, physical mass, surface height, and zero-velocity surface. Meanwhile, we recognize that there are five equilibrium points around Minerva, four of which are external, and one is internal. Two of the external equilibrium points are stable and near the yy-axis, while two external equilibrium points are unstable and near the xx-axis. In addition, we study the changes in the number, position, and topological case of the equilibrium points when changing the spin speed and the density. We calculate the gravitational force acceleration of the polyhedron model, and we back up our calculations by simulating the orbit of one moonlet under the gravitational force acceleration of Minerva. With the simulation result, we demonstrate the existence of stable orbits around Minerva.

Objective Lunar laser ranging has made outstanding contributions to maintaining the earth-moon reference frame, understanding the earth-moon system, and testing general relativity theory. However, due to the influence of the moon's apparent libration, the array corner retroreflector installed on the moon 50 years ago could not determine the corner retroreflector that reflected the photons, which would introduce cm-level errors. To overcome this problem, the newly deployed single large-aperture laser corner retroreflector is the leading choice for the next generation of lunar corner cube retroreflectors (CCR). Since the single-aperture corner retroreflector has a smaller reflection area than the array type, the CCR has higher requirements for directing. In this study, we analyze the effective diffraction region of the next-generation CCR and the relationship with the laser beam incident conditions employing numerical simulation. Ignoring the influence of atmospheric and dihedral errors, the observation situation of the newly-arranged CCR by three ground stations is simulated. The CCR pointing is optimized using the Levenberg-Marquardt method. We hope that our basic strategy and findings can be helpful in the deployment of the new CCR on the lunar surface in the near future. Methods In this study, a mathematical model with an effective diffraction region (EDR) is developed first for a retroreflector based on its geometrical structure and vector form of reflection-refraction law. Through numerical simulation, the regularity of change for EDR is analyzed. Then, we select three typical areas as the locations of the new CCR in the future, i.e., the Chang' E-3 landing area, Mare Nectaris area, and Shacklten Crater area. In terms of ground stations, three places such as GRASSE, APOLLO, and YNAO, are selected for observation. The minimal angle between the normal direction of the CCR and laser emitted by the ground station is taken as the optimizing objective. The optimization process is performed using the Levenberg-Marquardt method. In addition, the observation condition characteristics of the three ground stations are analyzed. Results and Discussions Assuming the arrangement of the lunar reflector points to the earth' s center at date J2000.0, the angle changes between the three specific areas selected in this study and the laser beams emitted by the ground stations are shown in Figs. 5-7. Because the distance between the earth and the moon is much larger than their radii, the angles between different lunar regions and stations on the earth are almost the same. They also have the same period, similar to 2190.4 days. The moon's anomaly mainly determines this period. Mean anomaly (F) and the latitude parameter (l) are superimposed (l - F); that is, the apparent libration is the main reason for the angle change. In this paper, the Levenberg-Marquardt method is used to optimize the normal direction of the corner reflector surface. Taking the Shacklten Crater area as an example, the optimized angle is shown in Fig. 8. The maximum angle is reduced to similar to 10 degrees, and the corner retroreflector' s effective utilization can exceed 80%. Similar results can be obtained by calculating the normal direction of the reflective surface of the Chang' E-3 landing area and the Mare Nectaris area. The disturbance period of the angle change is caused by 2l - 2F, affected by the apparent libration. To further study the observational characteristics of the angular reflection of the lunar surface at different stations, we consider the effective diffraction area (the angular reflection aperture area is set to 1) cumulated monthly (27 days). The observation area is the same, related to the earth-moon distance as the main influencing factor. However, for the same placement area, the lower latitude APOLLO and YNAO laser lunar station have better observation effects than the high-latitude GRASSE station. This shows that building stations in low-latitude regions of the earth can improve the efficiency of lunar laser ranging observations. Conclusions In this study, the numerical simulation method is used to systematically analyze the changes of the effective diffraction area of the next-generation single lunar corner reflector under different laser beam incident conditions. The influence of different lunar corner retroreflector orientations on ground observations is comprehensively discussed. The Levenberg-Marquardt method is used to optimize the corner retroreflector orientations in three typical regions by simulating the real observation time. The results show that the moon' s apparent libration is the main influencing factor affecting the effective diffraction area. This effect can only be reduced by optimizing the orientation, and there is no way to eliminate it. Meanwhile, the observation efficiency of low-latitude laser lunar stations is significantly higher than that of high-latitude stations. In addition, China is located in the eastern part of Asia, forming an excellent complementary effect with the stations in European countries and the United States. The results suggest that we should fully utilize the favorable conditions at the two low-latitude stations, the 1.2 m laser lunar ranging station of Yunnan Observatories, Chinese Academy of Sciences and the Zhuhai Tianqin laser lunar ranging station, to make significant contributions in future lunar exploration and laser ranging experiments.

月球物理天平动是月球运动在空间的描述.确定月球物理天平动,可以推测物理天平动的激发与耗散机制,比如陨击、月震和核幔粘滞摩擦等,测定月球物理天平动对认识太阳系天体的起源、演化及结构等具有十分重要的意义.利用最新的INPOP19a历表数据,完成了对从历表提取的欧拉角到月球物理天平动的转换,得到的物理天平动数值分别与该系列历表INPOP17a以及DE430对比发现,不同历表的物理天平动之差存在稳定的周期.对比历表欧拉角的差别,计算出地心到月面反射器A15的距离最大有30 cm的差别,此结果对月球激光测距的预报精度有较大的影响,为后续高精度测月研究打下基础.研究结果表明,INPOP19a最为稳定,在月球物理天平动研究中推荐使用INPOP19a.