Potential Series Expansion Method (PSEM)

• Potential Series Expansion Method (PSEM) is an analytical–numerical technique that models gravitational fields of irregular, constant-density celestial bodies by decomposing them into tetrahedra.
• It utilizes a Legendre-polynomial series expansion of the Newtonian kernel (1/r) to calculate tetrahedral moments analytically and reconstruct the gravitational potential.
• The method separates the primary Keplerian term from non-central contributions, providing a precise framework for simulating the effects of shape irregularity in polyhedral celestial bodies.

Searching arXiv for papers defining or using “Potential Series Expansion Method” and closely related series-expansion methods. Potential Series Expansion Method (PSEM) is an analytical–numerical method for representing the external gravitational field of irregularly shaped, constant-density celestial bodies modeled as polyhedra. In the direct usage of the term, the method decomposes the body into tetrahedra, expands the Newtonian kernel $1/r$ in a Legendre-polynomial series, evaluates the resulting tetrahedral polynomial moments analytically, and reconstructs the total potential as a finite sum $U=U_0+U_1+\cdots+U_m$, where $U_0$ is the Keplerian term and higher $U_i$ are non-central contributions induced by shape irregularity. The literature also uses the synonymous label “Series Potential Expansion Method,” with the acronym PSEM retained (Mota et al., 25 Jul 2025).

1. Definition and domain of applicability

PSEM is formulated for the gravitational field of a homogeneous solid of constant density $\sigma$, with center