A Study of the Shape Difference between the Level Surfaces of the Oblate Spheroid and the Ellipsoid

A new study of the level surface equations of Bruns’ spheroid and Helmert’s spheroid is carried out in this paper. With the help of the computer algebra system Mathematica, the strict expressions of the level surface equations are derived using the method of power series expansion. Based on these expressions, actual differences between level surfaces of oblate spheroids and the ellipsoid are illustrated visually through numerical calculation and analysis, and the knowledge in previous literatures about this problem are clarified and corrected.