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《Acta Geodaetica et Cartographica Sinica》 2010-05
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Non-singular Expression of the Disturbing Gravity Gradients

LIU Xiaogang,WU Xiaoping,ZHAO Dongming,WU Xing Institute of Surveying and Mapping,Information Engineering University,Zhengzhou 450052,China  
The non-singular computational formulae of the first-and second-order derivatives of the Legendre functions of the colatitude and the m P-n m(cos θ)/sin θ are introduced,and the non-singular computational formula of m2P-n m(cos θ)/sin2 θ is also deduced.When taking the non-singular computational formulas of the first-and second-order derivatives of the Legendre functions of the colatitude and the m P-n m(cos θ)/sin θ,m2P-n m(cos θ)/sin2 θ into the computation of each component of the disturbing gravity gradients,the complex situation that the m equals to 0,1,2,and any other numerical values are also considered,and the non-singular particular computational models of each component of the disturbing gravity gradients are constructed.The simulation experimentation shows that the particular computational models constructed in this paper not only completely fulfill the precision demand of the computation of the current satellite gravity gradients,but also the models are steady,credible and easy to be programmable realized.
【Fund】: 国家自然科学基金(40774031);; 全国优秀博士论文专项基金(200344);; 卫星导航与定位教育部重点实验室(B类)开放基金(GRC-2009010);; 中国科学院动力大地测量学重点实验室开放基金(L06-06);; 信息工程大学博士生创新基金
【CateGory Index】: P223
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1 MENG JIA-CHUN; CAI XI-MEI(Institute of Geodesy and Geophysics,Chinese Academy of Sciences,Wuhan 430077, China)MENG WEI(Wuhan Documentation and Information Center, Chinese Academy of Sciences, Wuhan 430071, China);WALSH-FOURIER SERIES EXPANSION AND TRANSFORM FOR THE GRAVITATIONNAL POTENTIAL[J];Chinese Journal of Geophysics;1998-S1
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