摘要
本文利用数学建模思想与几何分析方法,将文献[1]中的一道高等数学例题进行拓展延伸,建立了地球同步静止轨道卫星(Geostationary satellite,GEO卫星)与地球空间关系的几何模型.利用几何分析方法得到了在地球赤道上方只有一颗GEO卫星时卫星信号覆盖地表区域面积和覆盖比例,并得出卫星信号完全覆盖整个地球赤道至少需要三颗GEO卫星的结论.然后进一步利用空间对称几何关系建立了三颗GEO卫星均匀分布在地球赤道上方时卫星信号覆盖区域面积的二重积分模型,借助Maltab程序求出了三种信号覆盖类型区域面积与覆盖比例.
In this paper,based on mathematical modeling idea and geometric analysis method,a geometric model between GEO satellite and earth surface is established by extending an advanced mathematics example[1].By means of geometric analysis,the area and ratio of the surface area covered by only one GEO satellite signal above the Earth's equator are obtained,and it is concluded that at least three GEO satellites are required for the satellite signal to completely cover the Earth's equator.And then,by the aid of the geometric symmetric relations,the double integral models of the earth surface covered by the satellite signal when the three GEO satellites are uniformly distributed over the Earth's equator are established.The coverage areas and ratios of three kinds of satellite signal covering ranges were calculated by use of Maltab program.
作者
周家全
许超
程泳杰
邢朝阳
ZHOU Jiaquan;XU Chao;CHENG Yongjie;XING Chaoyang(Department of Mathematics and Physics,Luoyang Institute of Science and Technology,Luoyang 471023,China)
出处
《高等数学研究》
2025年第6期73-78,共6页
Studies in College Mathematics
基金
河南省高等教育教学改革研究与实践重点项目(No:2024SJGLX0123)
洛阳理工学院2023年度“微项目”研究项目
洛阳理工学院2023年大学生课外学术科技作品研究项目
洛阳理工学院2022年度教育教学改革研究项目(2022JYYB-012)。
