2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167259In this paper, we describe an analytical method for treating uniformly rotating homogeneous rings without a central body in Newtonian gravity. We employ series expansions about the thin ring limit and use the fact that in this limit the cross-section of the ring tends to a circle. The coefficients can in principle be determined up to an arbitrary order. Results are presented here to the 20th order and compared with numerical results.10 pages, 5 figures, minor corrections. This paper has be combined with arXiv:0802.0081 and published in MNRAS, see arXiv:0808.2612AstrophysicsGeneral Relativity and Quantum Cosmologytext