Symbolic Expressions of Differences between Earth Radii

A systematic and comprehensive comparison of the five commonly used earth radii in geodesy and cartography is carried out, and the differences between the most common points of the earth radii, their corresponding maximum values, and the latitudes of equal points between them are derived with the help of computer algebraic systems. The symbolic expressions are expressed as a power series of the first eccentricity. Taking the CGCS2000 ellipsoid as an example, the differences between the commonly used earth radii are clarified to numerical values. The results show that the difference between the commonly used earth radii has a maximum at 90 degrees and a minimum at 0 degree. The difference between the average radius of curvature and the rectifying sphere radius is the biggest, and the difference between the average radius of curvature and the average sphere radius is the smallest. These results can provide a theoretical basis for corresponding research in the geosciences, space science, navigation and positioning.