---
title: Potential Series Expansion Method (PSEM)
url: https://www.emergentmind.com/topics/potential-series-expansion-method-psem
type: topic
---

# Potential Series Expansion Method (PSEM)

Searching arXiv for recent 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 [2507.19433].

## 1. Definition and domain of applicability

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

Source: https://www.emergentmind.com/topics/potential-series-expansion-method-psem