Using the improved Hotine integral to determine earth gravity field

doi:10.11947/j.AGCS.2023.20210442

Abstract

Abstract: To solve the singularity problem of Hotine integral in calculating the radial component of disturbing gravity at a low altitude, this paper analyzes the causes and effects of singularity in traditional Hotine integral, on which the nonsingular formula of Hotine integral is derived according to the partition principle. The basic idea of the new method is to divide the integral region into inner region and far region, and the inner region is regarded as a micro plane with equal disturbing gravity value, in which we integrate the integral kernel function directly to eliminate singularity, then the advantages of the new method are expounded theoretically. The numerical results show that compared with the traditional Hotine integral, the improved one is continuous in the whole integral region, and the singularity of radial disturbing gravity is eliminated near the surface, besides the accuracy increases with the altitude decreases. What's more, the input data turns to the disturbing gravity difference on the ground, which reduces the influence of remote ground disturbing gravity in the calculation results. Numerical results show the demand for ground disturbing gravity data of the improved Hotine integral is nearly 20 times lower than that of the traditional algorithm, and the lower the height, the lower the demand for the integral radius.In conclusion, the algorithm proposed in this paper is suitable for the calculation of low altitude earth gravity field with high efficiency.

Key words: disturbing gravity, Hotine integral, singularity, integral radius

CLC Number:

P223

FENG Jinkai, WU Xiaoping, WANG Qingbin, ZHAO Dongming, HUANG Ziyan. Using the improved Hotine integral to determine earth gravity field[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(3): 397-404.

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