Identifications of the coefficients of the Taylor expansion (second order) of periodic non-collision solutions for the perturbed planar Keplerian Hamiltonian system

The discussion of disordered Keplerian Hamiltonian systems in our previously published study, which we verified, is expanded upon in this article. The collision semicircular orbit, and at least one other symmetric orbit is mentioned in this article. The proofs are based on the circular orbital decomposition and implicit function theory, and they concur with the results provided by Ambrosetti A. and Coyi Zelati. In the second stage, I use the Lindsted-Poincar approach to discover an asymptote. The Taylor squared expansion coefficients for periodic solutions of non-collision, are now defined.This interferes With the Kepler-Hamiltonian system, which is a part of the planar Kepler-Hamiltonian system. Systems with perturbations execute a Taylor expansion of the modulus when a system is perturbed in the time frame of full resolution and the word epsilon.