A general triaxial ellipsoid is suitable to represent the reference surface of the celestial bodies. The transformation from the Cartesian to geodetic coordinates on the triaxial ellipsoid becomes an important issue in geodesy. In the literature, the vector iterative method and the Newton’s iterative method for solving the nonlinear system of equations or an algebraic fraction equation is applied to compute the geodetic coordinates, but may lead to the non-convergence regions. In this work, the universal algorithm including the Newton’s iterative solutions of an algebraic sextic equation for the points outside the equatorial plane and the analytic solutions for the points inside the equatorial plane are used to compute the geodetic coordinates. The numerical experiments show the algorithm is fast, highly accurate and well convergent. The algorithm is valid at any point inside and outside the celestial bodies including the points near the celestial bodies’ center and in the singular elliptical disc.

一般的三轴椭球体适合于代表天体的参考面。在三轴椭球体上从笛卡尔坐标到大地坐标的转换成为大地测量学中的重要问题。在文献中，使用向量迭代法和牛顿迭代法求解方程组或代数分数方程的非线性系统来计算大地坐标，但可能会导致非收敛区域。在这项工作中，使用通用算法来计算大地坐标，该通用算法包括针对赤道平面外的点的代数六边形方程的牛顿迭代解和针对赤道平面内的点的解析解。数值实验表明，该算法快速，准确，收敛性好。