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 深空探测学报  2016, Vol. 3 Issue (1): 41-46  DOI: 10.15982/j.issn.2095-7777.2016.01.006 0

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Xiao Y, Ruan X G, Wei R Y. Research on the Accuracy and Operation Time of Polyhedron Gravity Model Base on 433 Eros[J]. Journal of Deep Space Exploration, 2016, 3(1): 41-46. DOI: 10.15982/j.issn.2095-7777.2016.01.006.
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### 文章历史

Research on the Accuracy and Operation Time of Polyhedron Gravity Model Base on 433 Eros
XIAO Yao, RUAN Xiaogang, WEI Ruoyan
School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China
Abstract: This paper adopts the polyhedron gravity modeling methodto calculate the surface gravitational acceleration of 433 Eros using the 3D polyhedron shape models of 433 Eros published by the Planetary Data System(PDS). The accuracy and operation time with different facets of the 3D polyhedron gravity model are also analyzed. The experiments show that the time complexity of polyhedron gravity model is O(n). In the simulation of the guidance, navigation and controlfor landing on 433 Eros, using the shape model with 22 540-facetscan achieve a tradeoff between the computation rate and accuracy.Moreover, since the gravity acceleration can be computed in real-time, it can be used in the hardware-in-the-loop simulation.
Key words: gravity model    polyhedron model    asteroids    433 Eros
0 引 言

1 多面体模型的引力场建模

 $\begin{array}{l} U(r) = \frac{1}{2}G\rho \sum\limits_{e \notin edges} {r_e^{\rm{T}}} {E_e}{r_e} \cdot {L_e} - \\ \quad \quad \quad \frac{1}{2}G\rho \sum\limits_{f \notin facet{\rm{s}}} {r_f^{\rm{T}}} {F_f}{r_f} \cdot {\omega _f}n\\ \end{array}$ (1)

 $\begin{array}{l} g(r) = \nabla U(r) = - G\rho \sum\limits_{e \notin edges} {{E_e}{r_e} \cdot {L_e}} + \\ \quad \quad \quad G\rho \sum\limits_{f \notin facet{\rm{s}}} {{F_f}{r_f} \cdot {\omega _f}} \end{array}$ (2)
2 多面体法验证与结果分析

 图 1 16～48 km三维球空间内随机500个点引力加速度相对误差直方图 Fig. 1 Histogram of gravitational acceleration relative error of 500 points random sampling from sphere space with radian from 16～48 km
3 433 Eros表面引力加速度分布情况计算

 图 2 433 Eros表面引力加速度 Fig. 2 Surface gravitational acceleration of 433 Eros
 图 3 433 Eros表面重力加速度 Fig. 3 Surface gravitational acceleration of 433 Eros with centrifugal acceleration correction
4 多面体法计算时间和精度研究

 图 4 不同面数多面体模型运行时间和相对误差 Fig. 4 The execution time and relative error of polyhedron shapemodelswith different facets

 图 5 使用面数为22 540和200 700的多面体模型对探测器轨道仿真计算 Fig. 5 Orbit simulations of spacecraft with 22 540-facets and 200 700-facets polyhedralmodels
5 总 结

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