球面距离计算方法及精度比较

Research on Spherical Distance Computation and Accuracy Comparison

球面距离(角间距)计算是天文或地理学中极常用的计算之一,也是目标查找、锥形检索、交叉证认等方法的基础。数学上,通过球面几何可以直接计算出两点的距离,前人已经推导出了多个复杂程度不一的计算方法。但是由于计算机的精度有限,在进行数值计算时有舍入误差,导致公式计算结果出现偏差。对几个常用的球面距离计算公式进行了考察,测试并对比它们在不同计算环境下的精度与优缺点。此外还展示并比较了几种常用天文软件包、数据库的球面距离计算方法,以期有助于天文工作者选择适合自己当前需要的计算方法。

Spherical distance(Angular separation)calculation is commonly using in Astronomy and Geography.It is the foundation of object detecting,data query and cross-matching.The spherical distance can be computed by Spherical Geometry method,and people have deduced many formulas.But the precision of computer is limited,due to rounding error in the numerical computation.This article will inspect several widely used formulas,test and compare their results,and discuss their advantage and disadvantage.In addition,this article will demonstrate how to do distance calculation on several astronomical packages and databases.The purpose of this article is to help astronomers to find the suitable method to do their calculation.