月球重力场模型及应用研究
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摘要
月球重力场强烈地影响着绕月探测器的运行轨道,利用精细的月球重力场,探月项目设计者能够更好地设计探月航天器的轨道。探测月球重力场有利于更好地计算月球的大地测量与动力学常数,也有助于月球物理天平动的研究,在充分了解月球重力场的基础上,还可以精确地知道月球的质心和转动惯量,以进一步地确定月球的大地坐标系。此外,月球重力场还是月球内部物质的物理反映,通过研究月球重力场,可以更深入地认识月球的地质演化历史和地质结构。
本文以月球重力场为研究对象,结合现有的月球重力场模型,重点研究了评估月球重力场模型的理论与方法、月球扰动引力矢量的空间特征和频谱特性以及月面地形与重力场相关性等内容,分析推导了基于跟踪观测技术恢复月球重力场的条件和能力等方面的一些问题。论文的主要工作及创新有:
1)介绍了月球概况、坐标系、月球重力场区别于地球重力场的特点及它的表示方法,总结了恢复月球重力场的原理,其中涉及动力学模型、解算过程等方面内容。
2)研究了月面质量瘤区域地形与重力异常的负相关性问题。结合现有月球重力场模型解算时采用跟踪数据的特点,通过各模型重力异常的直观对比以及阶方差曲线与考拉准则曲线吻合情况的比较,对月球重力场模型的质量进行了评估。研究并提出了对模型进行可靠性分析的方法,通过计算模型的信噪比反映了各模型空间频谱信号和频谱误差的强度,对模型的可靠性做出分析。通过这些手段,探索了一套适用于评估月球重力场模型的理论与方法。
3)分析了月球扰动引力矢量随高度变化的特征,对探测器在低空环境中所受月球扰动引力的影响进行了探讨研究。通过分析扰动引力径向谱分量与高度有关的谱分布趋势,估计了谱分量信息随高度增加而衰减的特点及其在不同频段的谱敏感度,得到了敏感各频段位系数与所需探测器轨道高度的关系。研究了该谱分量不同频段的分布特性,并据此提出了在解算不同频段月球重力场模型位系数时对解算方法进行改进的思路。
4)在深入了解深空探测器跟踪观测的主要技术的前提下,确定了恢复一定阶次重力场模型的分辨率条件,推导得到月球极圆轨探测器恢复至不同阶次月球重力场模型沿纬度方向(星下点轨迹间距)和沿经度方向(采样间隔)的最低分辨率条件,并结合我国“嫦娥一号”的实际情况进行了讨论。分析了轨道参数的选取对恢复月球重力场模型的重要影响以及两种评估绕月探测器恢复月球重力场能力的方法。
Lunar gravity field has a strong effect on lunar-orbiters. With a refined lunar gravity field, designers can design orbits better. Lunar gravity field is useful in calculating constants of lunar geodetic survey and geodynamics and researching lunar libration. With a detailed knowledge of the lunar gravity field, the lunar's mass center and moment of inertia can be determined accurately, so as to establish lunar geodetic coordinate system. Besides, as it is also the physical consequence of inner substance, we can learn more on lunar geologic evolving history and geologic structure.
In this paper, through investigation of the latest lunar gravity field models, theories on lunar gravity field were analyzed, which include estimation methods of model, spatial and spectral characteristics of lunar disturbing gravity, correlation of lunar terrain and lunar gravity field. And the conditions and capability of lunar gravity field recovery were analyzed. The main works and innovations are as follows:
1) A brief introduction was made on the Moon, its coordinate system, and its gravity field. The emphasis was laid on the characteristics of lunar gravity field that differ from the Earth's gravity field as well as the expression of lunar gravity field. Theories on the recovery of the lunar gravity field were reviewed, which involve dynamic models and solutions.
2) The negative correlation of mascon terrain and gravity anomaly on lunar surface was studied. According to the tracking data of different models as well as by comparing the gravity anomaly of different models, RMS curves of the potential coefficients for models and Kaula curves, model quality was estimated. A method for model reliability analysis is proposed which estimates the model reliability by comparing the Signal-Noise Ratio of models that reflect the spatial frequency spectral signal and errors. Above all of these, a method of estimating lunar gravity field was proposed.
3) The characteristics of the disturbing gravity with respect to height in the lunar gravity field were analyzed. And the effects of lunar disturbing gravity on spacecraft in low lunar orbit were discussed. By investigation of the spectral distributions of the radial spectral components with respect to height, the spectral sensitivities at different frequencies were estimated, and the relations between potential coefficients that can be sensed and orbiter heights were estimated. Furthermore, improvements were proposed to solutions to model coefficients of the low frequency, middle-frequency and high-frequency parts of the lunar gravity field.
4) Requirements on resolutions for the recovery of certain degree and order model coefficient were determined, and the lowest requirements on longitudinal and latitudinal resolution were derived for the recovery of the lunar gravity field model up to different degree and order for a circular-polar lunar orbiter. Then discussions were made on "Chang' E" mission, and the effects of the selection of orbit parameters on the recovery of the lunar gravity field model were analyzed. Finally two methods were discussed for evaluation of the capability of lunar gravity field recovery using lunar orbiters.
本文以月球重力场为研究对象,结合现有的月球重力场模型,重点研究了评估月球重力场模型的理论与方法、月球扰动引力矢量的空间特征和频谱特性以及月面地形与重力场相关性等内容,分析推导了基于跟踪观测技术恢复月球重力场的条件和能力等方面的一些问题。论文的主要工作及创新有:
1)介绍了月球概况、坐标系、月球重力场区别于地球重力场的特点及它的表示方法,总结了恢复月球重力场的原理,其中涉及动力学模型、解算过程等方面内容。
2)研究了月面质量瘤区域地形与重力异常的负相关性问题。结合现有月球重力场模型解算时采用跟踪数据的特点,通过各模型重力异常的直观对比以及阶方差曲线与考拉准则曲线吻合情况的比较,对月球重力场模型的质量进行了评估。研究并提出了对模型进行可靠性分析的方法,通过计算模型的信噪比反映了各模型空间频谱信号和频谱误差的强度,对模型的可靠性做出分析。通过这些手段,探索了一套适用于评估月球重力场模型的理论与方法。
3)分析了月球扰动引力矢量随高度变化的特征,对探测器在低空环境中所受月球扰动引力的影响进行了探讨研究。通过分析扰动引力径向谱分量与高度有关的谱分布趋势,估计了谱分量信息随高度增加而衰减的特点及其在不同频段的谱敏感度,得到了敏感各频段位系数与所需探测器轨道高度的关系。研究了该谱分量不同频段的分布特性,并据此提出了在解算不同频段月球重力场模型位系数时对解算方法进行改进的思路。
4)在深入了解深空探测器跟踪观测的主要技术的前提下,确定了恢复一定阶次重力场模型的分辨率条件,推导得到月球极圆轨探测器恢复至不同阶次月球重力场模型沿纬度方向(星下点轨迹间距)和沿经度方向(采样间隔)的最低分辨率条件,并结合我国“嫦娥一号”的实际情况进行了讨论。分析了轨道参数的选取对恢复月球重力场模型的重要影响以及两种评估绕月探测器恢复月球重力场能力的方法。
Lunar gravity field has a strong effect on lunar-orbiters. With a refined lunar gravity field, designers can design orbits better. Lunar gravity field is useful in calculating constants of lunar geodetic survey and geodynamics and researching lunar libration. With a detailed knowledge of the lunar gravity field, the lunar's mass center and moment of inertia can be determined accurately, so as to establish lunar geodetic coordinate system. Besides, as it is also the physical consequence of inner substance, we can learn more on lunar geologic evolving history and geologic structure.
In this paper, through investigation of the latest lunar gravity field models, theories on lunar gravity field were analyzed, which include estimation methods of model, spatial and spectral characteristics of lunar disturbing gravity, correlation of lunar terrain and lunar gravity field. And the conditions and capability of lunar gravity field recovery were analyzed. The main works and innovations are as follows:
1) A brief introduction was made on the Moon, its coordinate system, and its gravity field. The emphasis was laid on the characteristics of lunar gravity field that differ from the Earth's gravity field as well as the expression of lunar gravity field. Theories on the recovery of the lunar gravity field were reviewed, which involve dynamic models and solutions.
2) The negative correlation of mascon terrain and gravity anomaly on lunar surface was studied. According to the tracking data of different models as well as by comparing the gravity anomaly of different models, RMS curves of the potential coefficients for models and Kaula curves, model quality was estimated. A method for model reliability analysis is proposed which estimates the model reliability by comparing the Signal-Noise Ratio of models that reflect the spatial frequency spectral signal and errors. Above all of these, a method of estimating lunar gravity field was proposed.
3) The characteristics of the disturbing gravity with respect to height in the lunar gravity field were analyzed. And the effects of lunar disturbing gravity on spacecraft in low lunar orbit were discussed. By investigation of the spectral distributions of the radial spectral components with respect to height, the spectral sensitivities at different frequencies were estimated, and the relations between potential coefficients that can be sensed and orbiter heights were estimated. Furthermore, improvements were proposed to solutions to model coefficients of the low frequency, middle-frequency and high-frequency parts of the lunar gravity field.
4) Requirements on resolutions for the recovery of certain degree and order model coefficient were determined, and the lowest requirements on longitudinal and latitudinal resolution were derived for the recovery of the lunar gravity field model up to different degree and order for a circular-polar lunar orbiter. Then discussions were made on "Chang' E" mission, and the effects of the selection of orbit parameters on the recovery of the lunar gravity field model were analyzed. Finally two methods were discussed for evaluation of the capability of lunar gravity field recovery using lunar orbiters.
引文
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[2]陈俊勇,宁津生等.在嫦娥一号探月工程中求定月球重力场问题[J].地球物理学报,2005,48(2):275-281.
[3]陈俊勇.月球大地测量学进展[J].大地测量与地球动力学,2004,24(3):1-6.
[4]陆仲连,吴晓平.人造地球卫星与地球重力场[M].北京:测绘出版社,1994.
[5]陆仲连.地球重力场理论与方法[M].北京:解放军出版社,1996.
[6]陆仲连,吴晓平等.弹道导弹重力学[M].八一出版社,1993.
[7]张传定.卫星重力测量--基础、模型化方法与数据处理算法[D].郑州:解放军信息工程大学测绘学院,2000.
[8]鄢建国.月球重力场研究及绕月卫星精密定轨[D].武汉:武汉大学,2007.
[9]鄢建国,平劲松,李斐,王威.应用LP165P模型分析月球重力场特征及其对绕月卫星轨道的影响[J].地球物理学报,2006,49(2):408-414.
[10]李斐,鄢建国,平劲松.月球探测及月球重力场的确定[J].地球物理学进展,2006,21(1):31-37.
[11]李斐,鄢建国,平劲松.月球重力场的确定及构建我国自主月球重力场模型的方案研究[J].武汉大学学报·信息科学版,2007,32(1):6-10.
[12]沈飞.利用视线加速度数据恢复月球近区重力异常的研究[D].武汉:武汉大学,2005.
[13]赵德军等.空间扰动引力的谱分析[J],海洋测绘,2005,25(2):6-8.
[14]程芦颖,许厚泽.外空扰动外空扰动引力计算方法的内在联系[J].测绘学院学报,2003,20(3):161-164.
[15]夏哲仁,盛宗琪,李迎春.外空扰动引力场的传播特性[J].地球物理学报,1998,41(4):484-493.
[16]陈石,张健.重力位场谱分析方法研究综述[J].地球物理学进展,2006,21(4):1113-1119.
[17]罗佳.利用卫星跟踪卫星确定地球重力场的理论和方法[D].武汉:武汉大学,2003.
[18]王正涛.卫星跟踪卫星测量确定地球重力场的理论与方法[D].武汉:武汉大学,2005.
[19]徐天河.利用CHAMP卫星轨道和加速度计数据推求地球重力场模型[D].郑州:解放军信息工程大学测绘学院,2004.
[20]罗佳.现有SST重力场模型的比较研究[J].武汉大学学报·信息科学版,2006,33(7):594-598.
[21]宁津生,罗佳.卫星跟踪卫星应用于月球重力场探测的模拟研究[J].航天器工程,2007,16(1):18-22.
[22]李迎春.利用卫星重力梯度测量数据恢复地球重力场的理论与方法[D].郑州:解放军信息工程大学测绘学院,2004.
[23]John G.Proakis,Dimitris G.Manolakis.数字信号处理:原理、算法与应用(第三版)[M].北京:电子工业出版社,2004.
[24]许才军等.地球物理大地测量学原理与方法[M].武汉:武汉大学出版社,2006.
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