A Study on the formation of the gravitational Model based on Point-mass Method

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Jianqiang Wang 1,* Zhiqi Yu 2

1. Institute of Surveying and Mapping, East China Institute of Technology, Jiangxi Fuzhou, China

2. Department of geotechnical investigation & surveying,Wuhan Municipal Engineering Design & Research Institute Co. Ltd, Wuhan, China

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2011.02.06

Received: 20 May 2010 / Revised: 25 Sep. 2010 / Accepted: 3 Nov. 2010 / Published: 8 Mar. 2011

Index Terms

Point-mass model, the local gravity field, the earth gravity model, disturbance gravity, gravity anomaly, truncation error


The virtual point-mass method has been widely used in dealing with the approximation of the local gravity field which is a difficult problem in internal currently. In this paper, the approximation theory of point-mass model is briefly introduced, and the characteristics of the elements in the coefficient matrix for the model construction are analyzed by numerical calculation. The observations of gravity anomaly is simulated from EGM2008 with degree and order 720 and the approximated region is 32~34Nand 103~105E. A four-tier point-mass model which is on the base of the geopotential model with degree and order 36 from low frequency to high frequency is applied to approximate the local earth’s gravity field. The results of the experiments show that the truncation error of gravity disturbance created by using the point-mass model is less than 2 mGal on the radial direction and there is an optimal truncation error for some certain spectrum gravity field in the space.

Cite This Paper

Jianqiang Wang, Zhiqi Yu,"A Study on the formation of the gravitational Model based on Point-mass Method", International Journal of Intelligent Systems and Applications(IJISA), vol.3, no.2, pp.38-44, 2011. DOI: 10.5815/ijisa.2011.02.06


[1] Heiskanen W A, Moritz H, “Physical Geodesy,” Freeman and Company, San Francisco, 1967.

[2] Bjerhammar A, “A New Theory of Geodetic Gravity” Trans. Roy. Inst. Tech, No.243, 1964.

[3] Bjerhammar A, “Discrete physical geodesy,” Rep No.380, Dept. of Geodetic Science and Surveying, The Ohio State University, Columbus, 1987.

[4] Paul, E. Needham,R.E., “The Formation and Evaluation of Detailed Geopotential Models based on Point Masses,” Report No.149,Dept. of Geodetic Science and Surveying,The Ohio State University,1970.

[5] Sunkel. H., “The Generation of a Mass Point Model from Surface Gravity Data,” Report No.353, Dept. of Geodetic Science and Surveying, The Ohio State University, December 1983.

[6] Wu Xiao-ping, “Point-Mass Model of Local Gravity Field,” Acta Geodaetica et Cartographica Sinica, 1984, 13rded., vol. 4, pp. 250-258.

[7] Wen Han-jiang, “The Finite Element Models of Earth’s Gravity Field,” Science of Surveying and Mapping, 1993, vol. 1, pp. 41-47.

[8] Zhao Dong-ming, “Approximation of the Earth’s outer Gravity Field and State Estimation of Gravity Satellite,” Wuhan University, Wuhan, 2009.

[9] Zhang Hao, Wu Xiao-ping, Zhao Dong-ming, “A Study on Polynomial Fitting of Computing Space Disturbing Gravity with Point-Mass Model,” Science of Surveying and mapping, 2007, 32rded., vol. 4, pp. 42-45. 

[10] Pavlis, N.k., Holmes,S.A., Kenyon,S.C., John K. F., “An Earth Gravitational Model to Degree 2160: EGM2008,” Presented at the 2008general assembly of the European Geosciences Union, Vienna, Austria, 2008, pp. 13-18.

[11] Li Zhao-wen, Zhang Chuan-ding, Lu Yin-long, Li Jian-wei, “Establishment of the combined Point Mass Model Considering Spectrum Characteristic,” Journal of institute of surveying and mapping, 2004, 21rded., vol. 3, pp. 166-168. 

[12] Zhang Xiao-lin, Zhao Dong-ming, Wang Qin-bin, “Precise Determination and Approximation Analysis of Disturbing Gravity Field,” Journal of Geomatics Science and Technology, 2009, 26rded., vol. 3, pp. 212-215. 

[13] Li Jian-cheng, Chen Jun-yong, Ning Jin-sheng, Chao Ding-bo, “The Earth’ Gravity Field Approximation Theory and China’s 2000 quasi-geoid Determination,” Wuhan university press, Wuhan, 2003. 

[14] Huang Mo-tao, Guan Zheng “Test and Construction of Disturbing Point Masses Model,” Hydrographic Surveying and mapping, 1995, vol. 2, pp. 16-24.

[15] Tscherning C.C. “A Not e on the Choice of Norm when Using Collocation for the Computati on of Approximations to the Anomalous Potential,” Bull Geod, 1977, vol.55, pp. 137-147.

[16] Wang Jianqiang, Zhao Guoqiang, Zhu Guangbin, “Analysis of common Computing Methods of ultra-high Degree and Order fully normalized associated Legendre Function,” Journal of Geodesy and Geodynamics, 2009, 29rded., vol. 2, pp. 126-130.