球冠缺面积的一种数值积分方法与具体应用

A numerical integration method for calculating the area of a spherical crown part and its application

在有限场地内建造多架射电望远镜,可共享高精度时频标准、高数据率传输网络与设施,以及其他基础支撑设施、测试仪器和运行维护资源等,但是必须精确评估射电望远镜彼此之间的遮掩问题。结合具体工程实践,本文提出了射电望远镜外接球面的概念,给出了球冠缺(球冠被平面截取后的剩余部分)面积的一种积分表达式和数值积分方法,推演了积分结果的解析表达式,交叉检验了数值积分结果与解析表达式的正确性,并具体应用于两射电望远镜的互掩分析。该计算结果还可应用于后续天文观测的计划编排。

Multiple radio telescopes within a limited size of site can share high-precision time-frequency standards,high data rate transmission networks,and other basic support facilities,test instruments,operation and maintenance resources,but the shielding between radio telescopes must be accurately evaluated.Based on specific engineering practice,this paper presents the concept of the external spherical surface of the radio telescope,gives an integral expression and numerical integration method for the area of the spherical crown part(the remaining part after the spherical crown is intercepted by a plane),and deduces the analytical expression of the integral result.The correctness of the numerical integration result and the analytical expression is crossly checked,and the method is specifically applied to the mutual shielding estimation of two radio telescopes.The analysis results can also be used in the scheduling of subsequent astronomical observations.