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SCIENCE CHINA Orbit Determination for Chang'e-2 Lunar Probe And SCIENCE CHINA Physics, Mechanics & Astronomy • Article • March 2012 Vol.55 No.3: 514–522 doi: 10.1007/s11433-011-4596-2 Orbit determination for Chang’E-2 lunar probe and evaluation of lunar gravity models LI PeiJia1,2*, HU XiaoGong1*, HUANG Yong1*, WANG GuangLi1, JIANG DongRong1, ZHANG XiuZhong1, CAO JianFeng1,2,3 & XIN Nan1,2 1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; 2 Graduate University of Chinese Academy of Sciences, Beijing 100049, China; 3 Beijing Aerospace Control and Command Center, Beijing 100094, China Received September 28, 2011; accepted October 26, 2011; published online February 1, 2012 The Unified S-Band (USB) ranging/Doppler system and the Very Long Baseline Interferometry (VLBI) system as the ground tracking system jointly supported the lunar orbit capture of both Chang’E-2 (CE-2) and Chang’E-1 (CE-1) missions. The tracking system is also responsible for providing precise orbits for scientific data processing. New VLBI equipment and data processing strategies have been proposed based on CE-1 experiences and implemented for CE-2. In this work the role VLBI tracking data played was reassessed through precision orbit determination (POD) experiments for CE-2. Significant improve- ment in terms of both VLBI delay and delay rate data accuracy was achieved with the noise level of X-band band-width syn- thesis delay data reaching 0.2–0.3 ns. Short-arc orbit determination experiments showed that the combination of only 15 min’s range and VLBI data was able to improve the accuracy of 3 h’s orbit using range data only by a 1–1.5 order of magnitude, confirming a similar conclusion for CE-1. Moreover, because of the accuracy improvement, VLBI data was able to contribute to CE-2’s long-arc POD especially in the along-track and orbital normal directions. Orbital accuracy was assessed through the orbital overlapping analysis (2 h arc overlapping for 18 h POD arc). Compared with about 100 m position error of CE-1’s 200 km200 km lunar orbit, for CE-2’s 100 km100 km lunar orbit, the position errors were better than 31 and 6 m in the radial direction, and for CE-2’s 15 km100 km orbit, the position errors were better than 45 and 12 m in the radial direction. In addi- tion, in trying to analyze the Delta Differential One-Way Ranging (DOR) experiments data we concluded that the accuracy of DOR delay was dramatically improved with the noise level better than 0.1 ns and systematic errors better calibrated, and the Short-arc POD tests with DOR data showed excellent results. Although unable to support the development of an independent lunar gravity model, the tracking data of CE-2 provided evaluations of different lunar gravity models through POD. It is found that for the 100 km100 km lunar orbit, with a degree and order expansion up to 165, JPL’s gravity model LP165P did not show noticeable improvement over Japan’s SGM series models (100×100), but for the 15 km×100 km lunar orbit, a higher de- gree-order model can significantly improve the orbit accuracy. Chang’E-2, VLBI, orbit determination, lunar gravity field PACS number(s): 95.10.Eg, 95.40.+s, 95.55.Pe, 95.75.Kk ,96.20.Jz Citation: Li P J, Hu X G, Huang Y, et al. Orbit determination for Chang’E-2 lunar probe and evaluation of lunar gravity models. Sci China-Phys Mech Astron, 2012, 55: 514522, doi: 10.1007/s11433-011-4596-2 The Chang’E-2 (CE-2) probe was launched on October 1, came a lunar satellite on a polar, near circular orbit with an 2010. After nearly 5 d trans-lunar journey, it was captured altitude of approximately 100 km. On October 26, 2010, by the Moon on October 6, 2010, and then successfully be- CE-2 descended to 15 km to obtain photographs of the Sinus Iridum area. CE-2 is the second lunar probe of China. *Corresponding author (email: LI PeiJia: [email protected]; HU XiaoGong: hxg@shao. Compared to Chang’E-1 (CE-1) it was directly injected into edu.cn; HUANG Yong: [email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2012 phys.scichina.com www.springerlink.com Li P J, et al. Sci China-Phys Mech Astron March (2012) Vol. 55 No. 3 515 the trans-lunar orbit with the objectives to demonstrate key tracking technology is recommended in deep space explora- technologies for lunar landing, such as X-band tracking and tions with the advantages of low transmitting energy de- control, high resolution imaging and so on. Useful method- mand on-board and simple processing system on the ground. ology and software was developed for the mission and prac- In the CE-2 mission, X-band tracking and control experi- tical experience in engineering was accumulated, which ments were implemented and the DOR data was provided benefits the follow-on deep space explorations of China. by the VLBI system [8]. Both the Unified S-Band (USB) range/Doppler system The altitude of CE-1’s nominal lunar orbit was about 200 and Very Long Baseline Interferometry (VLBI) system km; however, in the CE-2 mission the altitude was lowered were used in CE-1 and CE-2 missions. Since the VLBI to about 100 km for better image resolution, and it even technology is able to provide high accuracy observations descended to 15 km to complete the close-up imaging task through differential interferometry and has no demand for for Sinus Iridum area during October 26–29, 2010. As the up-link transmission, it is a helpful supplement to radio altitude dropped, the orbital perturbation of lunar gravity on range/Doppler measurements. During the last 5 years, Chi- the satellite increased, and the precision orbit determination nese VLBI Network (CVN) has accumulated artificial (POD) accuracy of lunar orbit satellite is limited by the ac- spacecraft tracking experience for both Earth observation curacy and resolution of the lunar gravity model. As an in- satellites and deep space exploration spacecrafts, such as dependent data set, the tracking data of CE-2 was unable to TanCe-1 [1], COMPASS navigation satellites [2], CE-1 [3], support the development of an independent lunar gravity SMART-1 and Mars Express [4]. model; however, it can provide useful evaluations on dif- In the CE-2 mission, one of the important improvements ferent lunar gravity models through POD. of VLBI system was using the Digital Base-Band Converter In this paper, POD of CE-2 on various lunar orbits is stu- (DBBC) in place of the Analog Base-Band Converter died using different tracking data combinations, with an (ABBC) used in the CE-1 mission. Shanghai Astronomical emphasis on contributions of the improved VLBI tracking Observatory (SHAO) [5] started to develop DBBC a few data. The DOR data of the X-band tracking and control years before hoping to overcome the non-linear phase- system experiments are also analyzed. Performance of dif- frequency response of ABBC for better accuracy. After ferent gravity field models is discussed through POD. Orbit determinations are processed with a specifically modified numerous experiments and observational trials, DBBC was version of GEODYNII [9]. This paper is structured as fol- proved to satisfy design requirements and successfully ap- lows. The VLBI data improvements and the results for orbit plied in the CE-2 mission. determination of the CE-2 satellite are described in sect. 1. Post-processing strategies of the VLBI system were also The analysis of X-band tracking experiment is presented in improved. During the CE-1 and CE-2 missions, two obser- sect. 2. The evaluation of different gravity field models is vation modes were available [6]: real-time mode and post- described in sect. 3, and conclusions follow in sect. 4. processing mode. For the real-time mode, VLBI observa- tions were processed in less than 5 min after the reception of the 500 kHz bandwidth S-band signals. In this mode, the 1 POD of CE-2: analysis and discussion observations of extragalactic radio sources (i.e., quasars) before the satellite tracking arcs were used to correct sys- According to the principle of VLBI, the time delay between temic errors such as receiver delay, clock offset and drifts. the arrivals of the same wave-front at two antennae (the The quasar observations last about 1 or 2 h while satellite delay ) and the temporal rate of the change of the time tracking arcs could be from 8 to 12 h; hence significant time delay (the delay rate ) are measured via radio signal in- varying systemic errors remained and deteriorated the orbit terference. As we know, VLBI technology is able to obtain determination accuracy [7]. As an improvement, in the extremely high accurate observations, and different from CE-2 mission, in conjunction with quasars, long time series most range/Doppler tracking systems, uplink transmission is (from 5 to 7 d) of GPS data were also used to correct the not necessary. Furthermore, weak signal very far away is VLBI station clock drifts, and resulting in more precise es- picked up with large antennas. For the above reasons, VLBI timates of the systemic errors thanks to the stability of the is a useful supplement to usual radio range and velocity GPS time series. Different from the real-time mode, in the measurement techniques and can be applied in lunar and post-processing mode, quasar observations both before and deep space explorations. Simulation results show that joint after satellite tracking arcs were used to correct the clock orbit determination using VLBI and range/Doppler data can drift, which could help to achieve higher accuracy of VLBI improve the POD accuracy [9–11].
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