We propose a novel method for determining the radius of a spherical surface based on the distances measured between points on this surface. We consider the most general case of determining the radius when the distances are measured with errors and the sphere has random deviations from its ideal shape. For the solution, we used the minimally necessary four points and an arbitrary N number of points. We provide a new closed form solution for the radius of the sphere through the matrix of pairwise distances. We also determine the standard deviation of the radius estimate caused by measurement errors and deviations of the sphere from its ideal shape. We found optimal configurations of points on the sphere that provide the minimum standard deviation of the radius estimate. This paper describes our solution and provides all the mathematical derivations. We share the implementation of our method as open source code at https://github.com/boris-sukhovilov/Sphere_Radius.

翻译：我们提出了一种基于球面上点间测量距离来确定球面半径的新方法。我们考虑了在距离测量存在误差且球体存在随机偏离理想形状的情况下确定半径的最一般情形。求解时，我们使用了最少必需的四个点以及任意N个点。我们通过成对距离矩阵给出了一种新的球体半径闭式解。我们还确定了由测量误差和球体偏离理想形状引起的半径估计标准差。我们找到了能在球面上提供最小半径估计标准差的点最优配置。本文描述了我们的解决方案并提供了所有数学推导。我们在 https://github.com/boris-sukhovilov/Sphere_Radius 以开源代码形式分享了本方法的实现。