利用视线加速度数据恢复月球近区重力异常的研究
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摘要
月球重力场作为月球的主要物理特征之一,在月球的研究中具有非常重要的作用。月球重力场知识是月球探测器飞行轨道的设计和环月轨道的精确确定的重要前提,同时也是精确确定月球大地参考框架的基础。精确的月球重力场也是研究月球内部构造、月球演化历史,以及开发月球资源的基础信息。
本文对各个时期的月球探测计划进行了深入研究,并着重分析了月球重力场的确定方法,以视线加速度来确定月球近区重力场的直接方法作为主要研究内容。通过“Lunar Prospector”扩展任务获得的视线加速度数据,利用分步最小二乘的方法计算月球近区的重力异常。最后将计算结果和现今最高阶次的月球重力场模型LP165进行了比较和分析,得出标准差在纬度-75°～75°范围内为±27.354mGal,75°～85°,-85°～-75°范围内为±61.965mGal的精度,从而验证了该解算方法的可行性和可靠性。
As one of the moon's main physical features, lunar gravitational field plays a very predominant role in the study of the moon. The knowledge of the lunar gravitational field is the precondition of the lunar satellite orbit's designment and precise determination, and it is the base of the foundation of the lunar geodetic reference frame. In addition, the accurate lunar gravitational field is the essential information of studying the lunar internal structure, the evolution history and the exploitation of moon's resource as well.In this thesis, the past lunar exploration missions are described in detail, and the methods of determining the lunar gravitational field are analyzed in particular. Then the direct method is selected as the main research object, which processes the line-of-sight acceleration data from the Lunar Prospector extended mission using multiple step least square fitting method. Finally, the gravity anomaly of the nearside is obtained, and is compared with the latest lunar gravitational model LP165. It showsthat the standard deviation in the domain -75° ~ 75° is ±27.354 mgal, and75° ~ 85°,-85° —75° is ±61.965 mgal, which verifies the feasibility and reliability of this method.
本文对各个时期的月球探测计划进行了深入研究,并着重分析了月球重力场的确定方法,以视线加速度来确定月球近区重力场的直接方法作为主要研究内容。通过“Lunar Prospector”扩展任务获得的视线加速度数据,利用分步最小二乘的方法计算月球近区的重力异常。最后将计算结果和现今最高阶次的月球重力场模型LP165进行了比较和分析,得出标准差在纬度-75°～75°范围内为±27.354mGal,75°～85°,-85°～-75°范围内为±61.965mGal的精度,从而验证了该解算方法的可行性和可靠性。
As one of the moon's main physical features, lunar gravitational field plays a very predominant role in the study of the moon. The knowledge of the lunar gravitational field is the precondition of the lunar satellite orbit's designment and precise determination, and it is the base of the foundation of the lunar geodetic reference frame. In addition, the accurate lunar gravitational field is the essential information of studying the lunar internal structure, the evolution history and the exploitation of moon's resource as well.In this thesis, the past lunar exploration missions are described in detail, and the methods of determining the lunar gravitational field are analyzed in particular. Then the direct method is selected as the main research object, which processes the line-of-sight acceleration data from the Lunar Prospector extended mission using multiple step least square fitting method. Finally, the gravity anomaly of the nearside is obtained, and is compared with the latest lunar gravitational model LP165. It showsthat the standard deviation in the domain -75° ~ 75° is ±27.354 mgal, and75° ~ 85°,-85° —75° is ±61.965 mgal, which verifies the feasibility and reliability of this method.
引文
[1] Gunter Seeber著,赖锡安等译.卫星大地测量学.北京:地震出版社,1998.
[2] 郭俊义.地球物理学基础.北京:测绘出版社,2001.
[3] 海斯卡涅,莫里斯著,卢福康,胡国理译.物理大地测量学.北京:测绘出版社,1979.
[4] 胡明城.现代大地测量学的理论及其应用.北京:测绘出版社,2003.
[5] 胡明城,鲁福.现代大地测量学(上,下).北京:测绘出版社,1994.
[6] 孔祥元,郭际明,刘宗泉.大地测量学基础.武汉:武汉大学出版社,2001.
[7] 李建成,陈俊勇,宁津生,晁定波.地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社,2003.
[8] 刘林.航天器轨道理论.北京:国防工业出版社,2000.
[9] 陆仲连,吴晓平.人造地球卫星与地球重力场.北京:测绘出版社,1994.
[10] 平劲松,松花田英夫,日置幸介,坪川恒也等.今后几年的月球探测和月球科学.云南天文台台刊,(1):119—125,2003.
[11] Ananda M. E. Lunar Gravity: A Mass-point Model. J. Geophys. Res., 82(20), 3049-3064, 1977.
[12] Bills B. G., and Ferrari A. J.. A Harmonic Analysis of Lunar Gravity, J. Geophys. Res., 85(B2), 1013-1025, 1980.
[13] Binder A. B.. Lunar Prospector: Overview. Science, 281, 1475-1476, 1998.
[14] Cook. Lunar Polar Topography Derived from Clementine Steroimages. J. Geophys. Res., 105, 12023-12033, 2000.
[15] Dan McKenzie and Francis Nimmo. Elastic Thickness Estimates for Venus from Line of Sight Accelerations. ICARUS, 130, 198-216, 1997.
[16] David N. Barnett, Francis Nimmo, Dan McKenzie, Elastic Thickness Estimates for Venus Using Line of Sight Accelerations from Magellan Cycle 5. Icarus, 146, 404-419, 2000.
[17] Ferrari A. J.. Luanr gravity: A Harmonic Analysis. J. Geophys. Res., 82(20), 3065-3084, 1977.
[18] Ferrari A. J., Ananda M. P.. Luanr gravity: A Long-term Keplerian Rate Method. J. Geophys. Res., 82(20), 3085-3097, 1977.
[19] Iwata T., Hanada H., Kawano N, Takano T., Namiki N.. Global Lunar Gravity Mapping Using SELENE Sub-satellites. Workshop on Moon Beyond 2002, 2002.
[20] John. D. Anderson, Gerald Schubert, et al. Science, 305, Discovery of Mass Anomalies on Ganymede, 989-991, 2004.
[21] Kaula W. M.. Theory of Satellite Geodesy. Waltham-London: Blaisdell Publishing Company, 1966.
[22] Konopliv A. S., Asmar S. W., Carranza E., Sjogren W. L., Yuan D. N.. Recent Gravity Models as a Result of the Lunar Prospector Mission. Icarus. 150, 1-18, 2001.
[23] Konopliv A. S., Binder A. B. et al . Improved Gravity Field of the Moon from Lunar Prospector. Science, 281, 1476-1480,1998.
[24] Lemoine, F. G. R., Smith D. E., Zuber M. T., Neumann G. A., Rowlands D. D.. A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and Other Tracking Data. J. Geophys. Res., 102,16339-16359,1997.
[25] Luncas Reindler, Jafar Arkani-Hamed. The Compensation State of Intermediate Size Lunar Craters. Icarus, 153, 71-88, 2001.
[26] Mcewen A. S., Robinson M.S., Mapping the Moon by CLEMENTINE. Adv.Space Res., 19(10), 1523-1533,1977.
[27] Noriyuki Namiki, Hideo Hanada, Tsuneya Tsubokawa, et al. Selenodetic Experiments of SELENE: Relay Subsatellite, Differential VLBI, and Laser Altimeter. Adv.Space Res., 23(11), 1817-1820,1999.
[28] Ping, Jinsong; Heki, Kosuke, Matsumoto, Koji and Tamura, Yoshiaka. A Degree 180 Spherical Harmonic Model for the Lunar Topography. Adv. Space Res., 31(11), 2377-2382, 2003.
[29] Rune Floberghagen, Johannes Bouman, et al. On the Information Contents and Regularization of Lunar Gravity Field Solutions. Adv. Space Res. 23(11), 1801-1807,1999.
[30] Rune Floberghagen. Lunar Gravimetry: Revealing the Far-Side. Kluwer Academic Publishers ,2002.
[31] Sagitov, M.U., Bodri B. et al. Lunar Gravimetry. International Geophysics Series, Academic Press,1986.
[32] Sibing He. CHINA'S Moon Project CHANG'E: Stratagem and Projects. Adv. Space Res. 31(11), 2353-2358, 2003.
[33] Simpson R. A.. Software Interface Specification for the Line of Sight Acceleration Profile Data Record (LPSAPDR). 1999.
[34] Smith D.E., M.T. Zuber, Neuman G. A. et al. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. 102,1591-1661,1997.
[35] Takayuki Sugano, Kosuke Heki. High Resolution Lunar Gravity Anomaly Map from the Lunar Prospector Line-of-sight Acceleration Data. Earth Planets Space, 56 (1), 81-86, 2003.
[36] Thomas R. W., Konopliv A. S.. The Topography and Gravity of Mare Serenitatis: Implications for Subsidence of the Mare Surface. Planetary Space Science, 49, 743-748, 2001.
[37] Tuckness D.G, Jost B., A Critical Analysis of the Numerical and Analytical Methods Used in the Construction of the Lunar Gravity Potential Model. Applied Mathematics and Computation, 71(1), 69-90,1995.
[38] Zuber M. T., Smith D.E., Lemoine F.G. et al. The Shape and Internal Structure of the Moon from the Clementine Mission. Science 266,1839-1843,1994.
[2] 郭俊义.地球物理学基础.北京:测绘出版社,2001.
[3] 海斯卡涅,莫里斯著,卢福康,胡国理译.物理大地测量学.北京:测绘出版社,1979.
[4] 胡明城.现代大地测量学的理论及其应用.北京:测绘出版社,2003.
[5] 胡明城,鲁福.现代大地测量学(上,下).北京:测绘出版社,1994.
[6] 孔祥元,郭际明,刘宗泉.大地测量学基础.武汉:武汉大学出版社,2001.
[7] 李建成,陈俊勇,宁津生,晁定波.地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社,2003.
[8] 刘林.航天器轨道理论.北京:国防工业出版社,2000.
[9] 陆仲连,吴晓平.人造地球卫星与地球重力场.北京:测绘出版社,1994.
[10] 平劲松,松花田英夫,日置幸介,坪川恒也等.今后几年的月球探测和月球科学.云南天文台台刊,(1):119—125,2003.
[11] Ananda M. E. Lunar Gravity: A Mass-point Model. J. Geophys. Res., 82(20), 3049-3064, 1977.
[12] Bills B. G., and Ferrari A. J.. A Harmonic Analysis of Lunar Gravity, J. Geophys. Res., 85(B2), 1013-1025, 1980.
[13] Binder A. B.. Lunar Prospector: Overview. Science, 281, 1475-1476, 1998.
[14] Cook. Lunar Polar Topography Derived from Clementine Steroimages. J. Geophys. Res., 105, 12023-12033, 2000.
[15] Dan McKenzie and Francis Nimmo. Elastic Thickness Estimates for Venus from Line of Sight Accelerations. ICARUS, 130, 198-216, 1997.
[16] David N. Barnett, Francis Nimmo, Dan McKenzie, Elastic Thickness Estimates for Venus Using Line of Sight Accelerations from Magellan Cycle 5. Icarus, 146, 404-419, 2000.
[17] Ferrari A. J.. Luanr gravity: A Harmonic Analysis. J. Geophys. Res., 82(20), 3065-3084, 1977.
[18] Ferrari A. J., Ananda M. P.. Luanr gravity: A Long-term Keplerian Rate Method. J. Geophys. Res., 82(20), 3085-3097, 1977.
[19] Iwata T., Hanada H., Kawano N, Takano T., Namiki N.. Global Lunar Gravity Mapping Using SELENE Sub-satellites. Workshop on Moon Beyond 2002, 2002.
[20] John. D. Anderson, Gerald Schubert, et al. Science, 305, Discovery of Mass Anomalies on Ganymede, 989-991, 2004.
[21] Kaula W. M.. Theory of Satellite Geodesy. Waltham-London: Blaisdell Publishing Company, 1966.
[22] Konopliv A. S., Asmar S. W., Carranza E., Sjogren W. L., Yuan D. N.. Recent Gravity Models as a Result of the Lunar Prospector Mission. Icarus. 150, 1-18, 2001.
[23] Konopliv A. S., Binder A. B. et al . Improved Gravity Field of the Moon from Lunar Prospector. Science, 281, 1476-1480,1998.
[24] Lemoine, F. G. R., Smith D. E., Zuber M. T., Neumann G. A., Rowlands D. D.. A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and Other Tracking Data. J. Geophys. Res., 102,16339-16359,1997.
[25] Luncas Reindler, Jafar Arkani-Hamed. The Compensation State of Intermediate Size Lunar Craters. Icarus, 153, 71-88, 2001.
[26] Mcewen A. S., Robinson M.S., Mapping the Moon by CLEMENTINE. Adv.Space Res., 19(10), 1523-1533,1977.
[27] Noriyuki Namiki, Hideo Hanada, Tsuneya Tsubokawa, et al. Selenodetic Experiments of SELENE: Relay Subsatellite, Differential VLBI, and Laser Altimeter. Adv.Space Res., 23(11), 1817-1820,1999.
[28] Ping, Jinsong; Heki, Kosuke, Matsumoto, Koji and Tamura, Yoshiaka. A Degree 180 Spherical Harmonic Model for the Lunar Topography. Adv. Space Res., 31(11), 2377-2382, 2003.
[29] Rune Floberghagen, Johannes Bouman, et al. On the Information Contents and Regularization of Lunar Gravity Field Solutions. Adv. Space Res. 23(11), 1801-1807,1999.
[30] Rune Floberghagen. Lunar Gravimetry: Revealing the Far-Side. Kluwer Academic Publishers ,2002.
[31] Sagitov, M.U., Bodri B. et al. Lunar Gravimetry. International Geophysics Series, Academic Press,1986.
[32] Sibing He. CHINA'S Moon Project CHANG'E: Stratagem and Projects. Adv. Space Res. 31(11), 2353-2358, 2003.
[33] Simpson R. A.. Software Interface Specification for the Line of Sight Acceleration Profile Data Record (LPSAPDR). 1999.
[34] Smith D.E., M.T. Zuber, Neuman G. A. et al. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. 102,1591-1661,1997.
[35] Takayuki Sugano, Kosuke Heki. High Resolution Lunar Gravity Anomaly Map from the Lunar Prospector Line-of-sight Acceleration Data. Earth Planets Space, 56 (1), 81-86, 2003.
[36] Thomas R. W., Konopliv A. S.. The Topography and Gravity of Mare Serenitatis: Implications for Subsidence of the Mare Surface. Planetary Space Science, 49, 743-748, 2001.
[37] Tuckness D.G, Jost B., A Critical Analysis of the Numerical and Analytical Methods Used in the Construction of the Lunar Gravity Potential Model. Applied Mathematics and Computation, 71(1), 69-90,1995.
[38] Zuber M. T., Smith D.E., Lemoine F.G. et al. The Shape and Internal Structure of the Moon from the Clementine Mission. Science 266,1839-1843,1994.