THE ADVANCEMENT OF LUNAR GRAVITY MODEL DUE TO THE DEVELOPMENT OF SPACE TRACKING TECHNIQUES

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1 CHINESE JOURNAL OF GEOPHYSICS Vol.60, No.5, 2017, pp: DOI: /cjg THE ADVANCEMENT OF LUNAR GRAVITY MODEL DUE TO THE DEVELOPMENT OF SPACE TRACKING TECHNIQUES LI Fei 1,2, HAO Wei-Feng 1, YAN Jian-Guo 2, SHAO Xian-Yuan 2, YE Mao 2, XIAO Chi 1 1 Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan , China 2 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan , China Abstract Based on the three modes of lunar spacecraft tracking techniques: Earth-based tracking mode, highlow satellite-to-satellite tracking mode and low-low satellite-to-satellite tracking mode, the development of lunar gravity models could be divided into 4 stages. First, we introduce the principle, technical characteristics of the different tracking modes, and the representative gravity models, and then make comments on these models precision. Further, through the comparison of gravity anomaly precision, characteristics and orbit determination precision from different stages lunar gravity field models, we conclude that: the advancement of space tracking techniques has significantly improved the precision of lunar gravity model and effectively promotes the understanding of lunar interior structure and the reliability of lunar satellite orbit determination. Finally, we analyze the deficiency of current lunar gravity models and give a perspective of future space tracking techniques. Key words Lunar gravity model; Tracking mode; Lunar inner structure; Precise orbit determination 1 INTRODUCTION The moon is the only natural satellite of the earth; hence, understanding the moon is the first step in deep space exploration. The long journey to the Moon started in 1959 when the Soviet Union launched the first human lunar probe Luna 1. Rapid development of space technologies has expanded research possibilities beyond the movements of moon and its nearside surface features but the entire surface and inner structures of the moon. Currently, more than 50 lunar satellites and probes have been launched by six countries and regions. Among these missions, probing the lunar gravity field is one significant scientific objective. The lunar gravity field is an external representation of the internal mass distribution of the moon, revealing the moon s internal structure and evolution (Li et al., 2006). As in-situ lunar gravity and seismic measurements are not readily available, the main approach to study internal structure and its evolution of the moon involves a combination of gravity and topographic data. Moreover, lunar gravity is the chief source of spacecraft orbit perturbation. Refinement of lunar gravity field models therefore is vital for precise spacecraft orbit determination and landing. An accurate lunar gravity field model is one of the required design specifications determining probe equipment loads. China has successfully launched lunar orbiting satellites-chang E-1 and Chang E-2, implemented soft landing detection through Chang E-3, and launched Chang E-5 Test satellite to provide on-orbit verification for Chang E-5 mission. From this premise, China will continue to carry out the moon sample return detection and exploration of Mars and asteroids. The study of lunar gravity field will make full use of the Chinese lunar exploration tracking data and maximize its scientific value, and could provide references for designing specific characteristic lunar exploration mission and other planetary exploration program (Li et al., 2007). As it is now still impossible to carry out large-scale in-situ gravity field measurement on the moon, the lunar gravity field could only be solved by means of spacecraft orbit perturbation. With the advancement and innovation in space tracking technologies, accuracy and resolution of lunar gravity field models have been improving. This paper reviews lunar gravity field modeling and divides its evolution into four stages, denoted by space tracking fli@whu.edu.cn *Corresponding author: haowf@whu.edu.cn

2 494 Chinese J. Geophys. Vol.60, No.5 technology innovations. We elaborate the distinctive space tracking technologies and representative gravity field models for each stage. Through analysis of gravity anomalies and precision orbit determination validation, we illustrate how technological innovations support scientific achievements. We conclude by presenting a perspective on future space tracking techniques, considering the deficiencies of the existing lunar gravity models. 2 THE FIRST STAGE THE CONSTRUCTION OF LOW-DEGREE LUNAR GRAVITY MODELS ( ) From 1959 to 1972, the United States and the Soviet Union launched around 45 lunar probes, including Project Apollo, the manned lunar landing project. This period can be regarded as the first peak in lunar exploration. The probes launched in this period were the Luna and Zond series satellites from the Soviet Union and the Lunar Orbiter and Apollo series sub satellites from the United States. The space tracking technique adopted ground-to-satellite tracking mode, i.e., the ground tracking station transmitted radio Doppler signal to the satellite, and the satellite transponded the signal back to the ground tracking station through a space borne transponder. If the transmitting station and the receiving station were the same, then, the measurement was two-way. If not, the measurement was three-way. The data types of two-way and three-way measurement included ranges and Doppler. Fig. 1 shows the schematic view of the space-tracking mode during the first stage of lunar exploration. Using satellite orbit tracking data accumulated during this period, researchers focused on the solution of low-degree lunar gravity field. The initial research on the lunar gravity field was based on tracking data of Luna 10 and Lunar Orbiter 1, launched separately by the Soviet Union and the United States in After August 1967, four more spacecrafts with different inclination and eccentricity, Lunar Orbiter 2-5, were tracked. The type of tracking data during this phase was limited to the Doppler frequency shift. Measurement was the count of Doppler cycles, then converted into radial relative velocity between the ground station and lunar spacecraft. The tracking satellites were mostly at high altitude and small inclination, and tracking data coverage was limited near the equator. Due to low quality of the tracking data, scarce number of satellites and limitations of computing power at that time, all of the lunar gravity models derived then were low-degree models. Analyzing the orbit tracking data by spherical harmonic expansion, Lorell et al. (1968) introduced an 8 4 model, Liu et al. (1971) presented a 15 8 model, and Michael et al. (1972) provided a model. Muller et al. (1968) determined acceleration in the line of sight direction by using differential Doppler data, and drew out the coarse gravity anomaly map of lunar nearside. He discovered the mascons based on this gravity field. The Apollo Uplinksignal Transmitingand receivingstation Lunarsatelite Downlinksignal Moon Receivingstation Earth Fig. 1 Schematic view of the space tracking mode for the first stage

3 Li F et al.: The Advancement of Lunar Gravity Model Due to the Development of Space Tracking Techniques and 16 sub satellites launched in the 70 s added new observation data. Integrating these data, Bills et al. (1980) presented a lunar gravity model. From the early lunar gravity models, we gain a rough understanding on the lunar inner mass distribution. Discovering mascons was a leap in perceptions about the moon. The gravity model, in combination with other tracking data and samples, greatly improved the understanding of the core, libration, and other physical properties of the moon. However, due to the limitation of measurement accuracy and the orbit geometry, many uncertainties remained in our understanding of the lunar gravity field. 3 THE SECOND STAGE LAUNCHING OF THE GRAVITY SATELLITE ( ) As the product of the Star Wars between the US and Soviet Union, a large number of lunar exploration probes were launched in the first stages, whose main scientific goal was not the lunar gravity field. With the end of the cold war, lunar exploration missions stopped. In 1989, the United States proposed to return to the moon, and thus began a second lunar exploration era (Bush et al., 1989). The United States launched the Clementine and LP (Lunar Prospector) lunar mission in 1993 and 1998, respectively. The lunar gravity field and global terrain model was one of the main scientific targets. Thus, we define this period as the second stage of the lunar exploration. During this period, the tracking mode used was still two-way or three-way range/rate measurement between ground station and satellite, but of higher measurement precision and longer tracking periods than that of the first stage. The altitudes of the satellites were lower, which greatly enriched the acquisition of the perturbation. With the improvement of computer processing capacities, the solution to the lunar gravity field models was also improved before launching the Clementine. Konopliv et al. (1993) integrated all history tracking data (Lunar Orbiter 1-5, Apollo 15,16 sub-satellite), and solved a degree 60 lunar gravity field model, Lun60d, with higher precision for orbit determination, and was used as a reference for Clementine tasks. Clementine was a polar orbit probe with large eccentricity (400 km 8300 km), displaying remarkable improvement in the uniform coverage of tracking data. Based on dynamic orbit determination principle, Lemoine et al. (1997) presented a degree 70 lunar gravity field model (GLGM-2), which had improved the precision of low order (n = 2 20) tesseral coefficients when compared with the existing models. Due to the high eccentricity of Clementine, the spatial distribution of tracking data was uneven, leading to strong Kaula constraints ( /n 2, n is the degree of the gravity field). Therefore, only the low degree coefficients were reliable, and the higher degree coefficient was derived from the mathematical constraints. Based on the gravity model from Clementine, Zuber et al. (1994) analyzed the internal structure of the moon, and studied the global isostatic compensation of the moon. In order to obtain more accurate middle and high frequency information in the gravity field, the United States launched LP in 1998 with a low altitude and circular polar orbit, which was a free flying small satellite in spin stabilization and usually carried out orbital maneuver once per two or three months. LP ran stably at a low orbital altitude (100 km for the 1-year nominal mission, and 30 km for the 6 month extended mission), and its tracking data distribution was relatively uniform. With LP nominal mission and other historical tracking data, Konopliv et al. (1999) solved a degree 100 gravity field model LP100J. Adding LP extended mission tracking data, Konopliv then calculated a degree 165 lunar gravity field model LP165P (Konopliv et al., 1998; Yan et al., 2006), which is the most complete until the most recent 122 degree (about coefficients). Treating the degree 122 model as a priori information, a degree 145 model (about 6000 coefficients) can be estimated, and relayed to degree 165 model (about 6000 coefficients). But, due to the lack of data from the far-side, the correlation of these coefficients is very strong and thus difficult to ascertain local estimation. The LP165P model has very little noise until degree 110, but at the higher degree, it shows a very clear noise in the spectrum of RMS. Compared to the LP100J (radial positioning accuracy is 2 m, the other direction is 20 m), the LP165P models are more suitable for spacecraft orbit determination. Based on the same data and better computing equipment, Konopliv et al. (2001) presented a complete degree 150 model LP150Q, whose solution was done

4 496 Chinese J. Geophys. Vol.60, No.5 at one time, without truncating potential coefficients. LP s tracking data has improved the understanding of the lunar gravity field and played an important role in the refinement of the lunar gravity field model. At that time, LP gravity models were the best when only based on the ground tracking mode. At the beginning of the Chinese Chang E mission, the LP models were still the best reference for the lunar gravity field, and were an important data source for studying the moon s inner core and the lunar crust structure (Ke et al., 2009; Li et al., 2009). 4 THE THIRD STAGE OBTAINING LUNAR FARSIDE GRAVITY FIELD CHARACTERI- STICS (2007) Degrees and orders of lunar gravity models progressively improved, as a result, accuracy and ability of orbit determination also improved significantly, playing a more important role in research on lunar geological and interior physical structure. An obvious problem, however, was that in the ground tracking mode, since all of the tracking data were restricted on lunar nearside and the Kaula constraint had to be applied when executing global gravity model solutions, these lunar gravity models could not describe global mass distribution and gravity field characteristics. Thus, Japan designed a new tracking mode, borrowing the Satellite-to-Satellite Tracking Mode from detection of the earth gravity field. In 2007, Japan launched the SELENE lunar probe into space, implementing lunar global observation by the HL-SST (High Low Satellite to Satellite Tracking) technique (Kikuchi, 2006), which could be considered as the third phase of lunar gravity field development. The innovation of the SELENE mission was that the High-Low Four-way Doppler mode was used to implement the direct measurement of lunar farside gravity, and Same Beam Interferometry technology (SBI) was adopted for the first time (Kikuchi et al., 2006; Ping et al., 2001). Figure 2 shows a schematic diagram of this space tracking technique, that tracks and measures the main low lunar orbiter (the orbit is a circular polar orbit whose altitude is 100 km) by a relay satellite of high orbit (polar orbit, 100 km 2400 km). When the main satellite orbiter moved on lunar nearside, it carried out two-way range and range-rate mode tracking measurements between the ground station and main satellite. When the main satellite orbiter ran on the lunar farside, the tracking measurement of the farside orbit was implemented by using the Four-way Doppler Link measurement mode between the ground station (only Usuda space tracking station), the relay satellite Rstar and the main satellite. Since only one earth tracking station was involved in the Four-way Doppler measurement mode, the positioning accuracy of relay satellite and main satellite could not be ensured with limited tracking data during the observation time. Thus, they could not implement the highest level detection of the far-side gravity field. To improve the accuracy of orbit determination of the relay satellite, a VLBI satellite (Vstar, polar orbit, 100 km 800 km) was added in this mission. Vstar and relay Earth Fig. 2 SELENE high-low measurement (a) and same beam measurement (b)

5 Li F et al.: The Advancement of Lunar Gravity Model Due to the Development of Space Tracking Techniques 497 satellite Rstar were used to carry out high accuracy relative positioning measurement with the Same Beam Interferometry mode. By eliminating system errors, including medium propagation and station receiving system errors, the accuracy of the Rstar orbit determination was improved to ensure the accuracy of Four-Way Doppler measurement. The normal mission phase of SELENE lasted about one year. Using first three months data, Namiki et al. (2009) derived a gravity model, SGM90d, whose accuracy was a substantial improvement over the LP100K model due to the direct tracking data from the lunar farside. LP100K s RMS error in orbit determination was 15 mm s 1 or so, but for SGM90d, it was 1 mm s 1. This model revealed large scale lunar farside gravity field characteristics, and helped identify annular gravity anomaly characteristics near impact basins, which were concealed by errors in the previous gravity models. Integrating complete four-way Doppler measurement data in normal missions, a degree 100 gravity field model, SGM100h, was given by Matsumoto et al. (2010). Compared with SGM90d, more refined farside gravity field characteristics were revealed by this model, which helped identify more new impact craters and basins (Matsumoto et al., 2010). The lunar exploration probes launched into space during the same stage of SELENE include Chinese Chang E-1 (2007), Indian Chandrayaan-1 (2008) and American LRO (Lunar Reconnaissance Orbiter, 2009). Chandrayaan-1 focused on lunar chemical elemental compositions, and LRO was mainly used to refine topographic models of the moon, and did not contribute to gravity field research. During the one year of orbit operations, Chang E-1 accumulated a large number of orbit tracking data (two-way range and range-rate), which contained abundant gravity field information, especially the low degree parameters (Yan et al., 2010; Yan et al., 2010). Combining Chang E-1, SELENE and other historical tracking data, Yan et al. (2012) derived a degree 100 gravity field model, CEGM02. As compared to the SGM100h model, CEGM02 improved medium and low degree and order terms significantly. Based on the lunar k 2 tidal love parameter solved by the SGM100h and CEGM02 models, Harada et al. (2014) suggested that there might be a melting layer of low viscosity at the core-mantle boundary of moon. 5 THE FOURTH STAGE HIGH PRECISION AND RESOLUTION GLOBAL GRAVITY FIELD RECOVERY ( ) The gravity information from the lunar farside was integrated into the solution of the gravity field model for the first time by using the SELENE high-low tracking mode data, thus greatly improving the accuracy and reliability of the lunar gravity field model. Nevertheless, the quantity of the four-way Doppler tracking data collected during the SELENE operation period was limited as only the Usuda station was involved in the observation, with an observation time restricted to less than one hour a day, and the tracking data was mainly distributed in the southern hemisphere. Thus, the precision and resolution improvement to the farside gravity field during the SELENE mission was rather limited, with the valid degree only up to 70 degree. The United States then launched the GRAIL (Gravity Recovery and Interior Laboratory) spacecraft in September This mission adopted another higher precision satellite-satellite tracking mode, namely Low-Low satellite-tosatellite tracking. This mode is similar to the earth gravity satellite GRACE, and is considered as the best mode for obtaining the orbit perturbation of both satellites. The implementation of the GRAIL mission can be regarded as the fourth stage in lunar gravitational field development. The high precision, global uniformly distributed inter-satellite Ka-Band Range Rate (KBRR) tracking data were obtained from GRAIL mission. Compared to the former station-to-satellite S-band measurement, the accuracy of KBRR was raised by nearly four orders of magnitude, reaching the level of 0.5 microns per second, which help to find the lunar mass anomaly. The orbits of the two satellites in the GRAIL mission were both circular polar orbits. They had an average altitude of about 50 km in the Primary Mission (PM) and 30 km in the Extended Mission (EM). Fig. 3 shows the satellite-tracking system of GRAIL mission. The S-band tracking data between the ground station and satellite permits satellite precise orbit determination, while the globally distributed KBRR data was used for high preciion gravity field recovery. The S-band measurements between

6 498 Chinese J. Geophys. Earth Moon Fig. 3 Schematic view of GRAIL s tracking mode Vol.60, No.5 the twin satellites were used for time synchronization. Compared to the SELENE mission that adopted a high-low tracking mode, the GRAIL mission provided richer types of tracking data, of higher precision and more uniform distribution. Using three months of PM measurement data, Zuber et al. (2013) published the GL0420A, a gravity field model up to degree 420. This model presents globally uniformly distributed high precision gravity field information for the first time, and presents more detailed gravity field characteristics of the lunar farside, including a large number of small scale craters and basins. Using this model, Wizoreck et al. (2013) re-estimated the thickness and density of the lunar crust, finding that the average lunar crust thickness is less than that previously estimated, only around 35 km. Then, JPL and GSFC presented the degree 660 model GL0660B (Konopliv et al., 2013) and GRGM660PRIM (Lemoine et al., 2013) respectively. As compared to the GL0420A model, the accuracy at the high degree of the gravity field model was further improved, and the gravity/topography correlation coefficient increased significantly. By synthesizing PM and EM data, JPL and GSFC presented other degree 900 gravity field models- the GL0900D (Konopliv et al., 2014) and GRGM900C (Lemoine et al., 2014). The 900 degree models made further improvements in the accuracy of high degree and order coefficients, their spatial resolution reaches 6 km, and their gravity/topography correlation is still close to 1 until the degree 700. Table 1 summarizes the gravity field models from the four stages and their representative tracking modes. Table 1 Typical Tracking Mode and Representative Gravity Models of Different Stages Periods of Representative Tracking time missions mode First stage Apollo lunar exploration era Typical models The features of Typical the models characteristics Sagitov Low degree, large scale gravity field Discovered the nearside mascons GLGM-2, LP100K Near-side high order gravity field model The elaboration of the nearside gravity field Ground tracking mode Second stage Clementine/LP Third stage SELENE High-low tracking mode SGM100h The global gravity field model Preliminary reveals large scale farside gravity characteristics Fourth stage GRAIL Low-Low tracking mode GRGM660PRIM Global high precision and high resolution model The elaboration of global gravity field 6 IMPROVED UNDERSTANDING OF LUNAR GRAVITY ANOMALY CHARACTERISTICS WITH DIFFERENT STAGES GRAVITY FIELD MODELS The development of tracking technology has improved the resolution and accuracy of lunar gravity field models, and promoted greater understanding of lunar gravity anomaly characteristics. We chose four gravity models, each representative of a different stage, the Sagitov16 16, LP100K, SGM100h, and GRGM660PRIM models to calculate the free-air gravity anomaly respectively, and analyzed the corresponding gravity field characteristics.

7 Li F et al.: The Advancement of Lunar Gravity Model Due to the Development of Space Tracking Techniques 499 Figure 4 shows the global free-air gravity anomaly as calculated by the four typical gravity models. We can see that because of the restrictions on the distribution and accuracy of the early tracking data as well as by the limited computer processing capability, the orders and accuracy of these lunar gravity field models are relatively low. Taking the Sagitov16 16 model as an example, we can only find typical mascons on the lunar nearside; however, the noise is relatively large with two noticeable noisy points on the farside. A lot of low orbit tracking data with high precision were obtained from LP mission, making it possible to improve the solution of lunar gravity field. Fig. 4 shows that mascons on lunar nearside are evident in the LP100K gravity anomaly map. Due to lack of farside tracking data, however, there are unmistakable band errors on lunar farside. Using the SGM100h model obtained from SELENE tracking data, we can further our understanding of the large-scale gravity anomalies distribution on the lunar farside and find new features of these gravity anomalies. In a typical mascon area on the lunar nearside, a positive gravity anomaly is surrounded by negative gravity anomaly. While in a typical mascon area on the farside, such as Korolev (4.5 S, 157 W), negative and positive anomalies distribute alternatively as ring form from center to the outer boundary. The newly revealed GRAIL gravity model GRGM660PRIM shows us more details of free-air gravity anomaly compared to previous lunar gravity field models. The GRGM660PRIM has no band errors as SGM100h produced by limitation of tracking data, reveals new details of impact basins, and shows that the lunar gravity and topography are highly correlated. 7 THE IMPROVEMENT OF LUNAR SATELLITE PRECISE ORBIT DETERMINATION WITH DIFFERENT STAGES OF THE GRAVITY FIELD MODEL In addition to the gravity anomaly characteristics, precise orbit determination can also be used to evaluate the accuracy and reliability of gravity field models derived at different tracking stages. Mazarico et al. (2013) determined the precise orbits of the LP, SELENE and LRO missions using different gravity field models. In this paper, we determined the precise orbit of Apollo 15 sub-satellite mission to evaluate the level of precision in different models. Apollo 15 sub-satellite was a lunar orbiting satellite launched after the Apollo 15 manned mission. It measured lunar surface topography via satellite laser ranging. The orbital eccentricity of Apollo 15 was high, with an orbit inclination of about 35, as opposed to the LP, SELENE, and LRO missions with orbit inclinations of about 90. For precise orbit determination of the Apollo 15 sub-satellites, estimated parameters included six orbital parameters, solar pressure coefficient, and systematic error of measurement. The Sagitov 16 16, LP100K, SGM100h and GRGM660PM models were used separately during this process. The measurement data included two-way and three-way Doppler. Fig. 5 shows the Doppler residuals from the four tested models. Table 2 also shows the means and RMS values of the residuals. Table 2 The statistical results of precise orbit determination residuals from different models (Unit: mm s 1 ) Sagitov LP100K SGM100h GRGM660PM Two way Doppler Mean value Residuals RMS Three way Doppler Mean value Residuals RMS As shown by Fig. 5, precise orbit determination results from early Sagitov model are poor. The low degree model Sagitov can only reflect long wavelength part of the lunar gravity field, thus impeding precise orbit determination in low orbit. Moreover, the Sagitov model solution did not include Apollo 15 sub-satellite tracking data. The residuals from these two models correspond to the big jump visible at the center of each graph in Fig. 5. This is because the satellite altitude is low but the coefficients of low degree and order are not able to absorb the gravity field information. A big jump does not appear in the case of the

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9 Li F et al.: The Advancement of Lunar Gravity Model Due to the Development of Space Tracking Techniques 501 Fig. 5 Precise orbit determination residuals from different models (a) Two-way range rate residuals from Sagitov; (b) Two-way range rate residuals from LP100K, SGM100h, and GRGM660PM; (c) Three-way range rate residuals from Sagitov; (d) Three-way range rate residuals from LP100K, SGM100h and GRGM660PM.

10 502 Chinese J. Geophys. Vol.60, No.5 GRGM660PM model as it is a high order solution and thus more conducive to orbit determination at lower altitudes. When using GRAIL model to deal with small inclination satellites, we can also get very good results, in contrast to the results reported by Li et al. (2011) as their research indicated that the lunar gravity model derived from polar satellite tracking data was not suitable for non-polar orbit satellite orbit determination. Our work shows that GRAIL satellite-to-satellite tracking data can significantly improve the accuracy of lunar gravity field models. 8 CONCLUSION AND OUTLOOK As can be seen from the history of lunar gravity field development, the improvement of each stage s gravity field model results from the tracking technology innovation, and this innovation is essentially the effective learning of the Earth s gravity field satellite detection technology, such as high-low satellite-to-satellite tracking technology, low-low satellite-to-satellite tracking technology and so on. Since the moon has no atmosphere outside, using the similar tracking method with the Earth satellite should be more effective. It is generally acknowledged that the precision and resolution of the lunar gravity field model is high enough through the satellite-to-satellite tracking mode. To obtain a more accurate lunar gravity field model, we believe that there are several directions to pursue: First, the low degree part of the lunar gravity field model could be improved. Fig. 6 shows power spectra and its difference in the gravity field model acquired by recent mission, in which figure (b) is an enlarged view of figure (a) for the first 100 degrees. A comparison of the difference between power spectra shows that the improvement in the low degrees by GRAIL mission is limited. The variance of C 20 (the second degree terms coefficient) given by the GRGM0660PM, is , while for the GRGM900C, it is When comparing with the CEGM02 (the variance of C 20 is ) that combines SELENE and Chang E-1 tracking data, the improvement for GRGM models is still not significant, considering that the accuracy of the higher order terms increases up to four orders of magnitude, while the improvement for the second order items is only two times higher. If the GRAIL, SELENE and other historical tracking data are further integrated, especially Chinese Chang E km altitude orbit tracking data, the precision of lower order terms coefficient could be further improved. Fig. 6 Power spectra and its difference from different gravity models

11 Li F et al.: The Advancement of Lunar Gravity Model Due to the Development of Space Tracking Techniques 503 Second, the American LRO satellite has already obtained the highest accuracy and resolution topographic data through the laser altimeter and narrow-angle/wide-angle camera. The topographic data resolution derived by LRO is higher than GRAIL gravity field model (Konopliv et al., 2014). Thus, the high-frequency gravitational field effect generated by topographic data can be used to validate gravity field models and to improve the high frequency part of existing lunar gravity field model. Third, to further improve the accuracy of lunar gravity field model, it is necessary to break from the data acquisition mode that only relies on the tracking technology, and innovate new ways of direct observation, such as gravity satellites with accelerometers or launching gravity gradiometry satellites similar to Earth observation systems GOCE. In addition, the most significant issue in lunar gravity field is the lack of adequate in-situ measurement on lunar surface to validate models. The four existing Apollo gravity measurement points are located at the Maria area, and the uncertainty of the position and accuracy is large. In future lunar exploration missions, laying gravity measurement points in the lunar Antarctic (Weifeng et al., 2012) or the Highlands region might be considered to expand the spatial distribution of ground measurement points to fundamentally improve the accuracy and reliability of the lunar gravity field models. ACKNOWLEDGMENTS This work was supported in part by the National Natural Science Foundation of China ( , ); the Natural Science Foundation of Hubei Province (2015CFA011). Lunar gravity field models used in this article are taken from the NASA PDS Geoscience Node Data center and JAXA Data Archive center. Part of the calculation used the SHTOOLS, and the Generic Mapping Tools (GMT) software is used to draw spherical projection maps. Thanks for the comments made by peer reviewers. References Bills B G, Ferrari A J A harmonic analysis of lunar gravity. Journal of Geophysical Research, 85(B2): , doi: /JB085iB02p Bush G H W Remarks on the 20th anniversary of the apollo 11 Moon landing. index.php?pid= Hao W F, Li F, Yan J G, et al Lunar polar illumination based on Chang E-1 laser altimeter. Chinese Journal of Geophysics (in Chinese), 55(1): 46-52, doi: /j.issn Harada Y, Goossens G, Matsumoto K, et al Strong tidal heating in an ultralow-viscosity zone at the core-mantle boundary of the Moon. Nature Geoscience, 7(8): , doi: /ngeo2211. Ke B G, Li F, Wang W R, et al Analysis of the lower mantle thickness and core size of lunar based on the solution of the Lane-Emden equation. Chinese Journal of Geophysics (in Chinese), 52(5): , doi: /j.issn Kikuchi F Differential phase delay estimation by same beam VLBI method [Ph. D. thesis]. Kanagawa, Japan: The Graduate University for Advanced Studies. Konopliv A S, Sjogren W L, Wimberly R N, et al A high resolution lunar gravity field and predicted orbit behavior. // AAS/AIAA Astrodynamics Specialist Conference. Victoria, B. C.: AIAA, Konopliv A S, Yuan D N Lunar prospector 100th degree gravity model development. // Proceedings of the 30th Annual Lunar and Planetary Science Conference. Houston, TX: Lunar and Planetary Institutes. Konopliv A S, Binder A B, Hood L L, et al Improved gravity field of the Moon from Lunar Prospector. Science, 281(5382): , doi: /science Konopliv A S, Asmar S W, Carranza E, et al Recent gravity models as a result of the Lunar prospect mission. Icarus, 150(1): 1-18, doi: /icar Konopliv A S, Park R S, Yuan D N, et al The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL primary mission. Journal of Geophysical Research: Planets, 118(7): , doi: /jgre

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