On the Fundamental Defects of Newton's Shell Theorem and the Necessity of the Cubic Partition Method

Newton’s shell theorem is the theoretical cornerstone for applying the law ofuniversal gravitation to celestial calculations. This paper demonstrates from threeaspects—geometric, physical, and logical—that the ”shell partition method” reliedupon by the theorem suffers from three fundamental defects: geometric mass loss(about 9.31%), systematic neglect of angular information, and complete eliminationof three-dimensional spatial configuration. These defects lead to unavoidable sys-tematic errors in gravitational calculations for non-spherical objects (such as galax-ies and irregular mass distributions). This paper also proposes the ”cubic partitionmethod” as an alternative, proving that it achieves 100% space filling, retains allgeometric configuration information, and is a more accurate and universal methodfor gravitational calculations.