Comparison Study of the Numerical Calculations of the Spherical Integral Based on Two Models

We present a new approach to proceed numerical integral on a sphere and derives the corresponding numerical integral formulas.If the condition of uniform distribution on the sphere is ignored,a general expression of the spherical numerical integral formula based on the irregular distribution of N points on a sphere is introduced,and some spherical numerical integral formulas,which are based upon different division approaches on a sphere,are unified.By numerical calculations,we compare and analyze the results under the grid division and uniform distribution with equal number of data points in models:in the case of constant spherical potential,and the more complicated potential distribution(EGM96) which approximates the real case better,the accuracy of calculations using the Thomson uniform distribution model is higher and better than that using the grid division model.