SSRScientific and Social Research2661-43322981-9946Bio-Byword Scientific Publishing Pty. Ltd.10.26689/ssr.v8i9.15768ArticleSynthesized Dual-Resonance Model for Revealing the Isotropic Uniform Symmetry (IUS) of Planetary Orbitshttps://artdesignp.com/journal/SSR/8/9/10.26689/ssr.v8i9.15768HeJason Tianyu,ChenColin Cheng,DengJames T. Q.2026892026-10-21Planetary Perturbations are caused by multi-body gravity and relativity. The first kind of perturbation method is to use a high-order numerical approximation or analytical series to obtain a result. Based on the SDP atom model, the study has developed a Synthesized Dual-Resonance model to describe orbital precession as the coupling of radial resonance and circumferential motion. The model has an integral form for angular momentum. Numerical simulations have shown that the shape of the orbit and its convergence properties at all frequencies are different, and cumulative orbits approach an isotropic, uniform, symmetric ring around a single dynamical center in the long-period limit. It has a relatively simple kinematic structure for quick orbit design and long-period prediction.Spiral Drift Precession Model (SDP), Isotropic Uniform Symmetry (IUS), Sole centrism of a stellar system, Closures of planetary orbits

[1] Russell JL, 1964, Kepler’s Laws of Planetary Motion: 1609–1666. The British Journal for the History of Science, 2(1) 1–24. [2] Thoren VE, Christianson JR, 1990, The Lord of Uraniborg: A Biography of Tycho Brahe. Cambridge University Press, Cambridge. [3] Plakhotnyk M, 2017, Kepler’s Laws with Introduction to Differential Calculus. arXiv preprint arXiv:1702.06537. [4] Marquis de Laplace PS, 1825, Traité de mécanique céleste (Vol. 5). Chez JBM Duprat, libraire pour les mathématiques, quai des Augustins. [5] Lagrange JL, 1853, Mécanique analytique (Vol. 1). Mallet-Bachelier. [6] Poincaré H, 1890, Sur le problème des trois corps et les équations de la dynamique. Acta mathematica, 13(1): A3–A270. [7] Einstein A, 1916, Die Grundlagen der allgemeinen. Relativitats− teorie. Annale der Physic, 1916(49): 769. [8] Brouwer D, Clemence GM, 2013, Methods of Celestial Mechanics. Elsevier. [9] Cowell PH, Crommelin AC, 1911, Investigation of the Motion of Halley’s Comet From 1759 to 1910. Greenwich Observations in Astronomy, Magnetism and Meteorology made at the Royal Observatory, Series 2, vol. 71, pp. O1-O84, 71, O1-O84. [10] Encke JF, 1851, Über eine neue Methode der Berechnung der Planetenstörungen. Königl. Akademie der Wissenschaften. Über eine neue Methode der Berechnung der Planetenstörungen. [11] Roy AE, 2020, Orbital motion. CRC Press. [12] Ceccaroni M, Biggs J, 2013, Analytic Perturbative Theories in Highly Inhomogeneous Gravitational Fields. Icarus, 224(1): 74–85. [13] Newton I, 1833, Philosophiae naturalis principia mathematica (Vol. 1). G. Brookman. [14] Murray CD, Dermott SF, 1999, Solar System Dynamics. Cambridge University Press, Cambridge. [15] Deng JTQ, 2023, A New Terahertz Source from the Wave Particle Duality Mechanism. The Journal of Engineering, 2023(1): e12217. [16] Deng J, 2022, Theoretically Proving the Quantization Hypothesis. Authorea Preprints. [17] Deng J, 2022, Theoretically Proving the Quantized Wave-Particle Duality. Authorea Preprint. [18] Deng JTQ, 2025, Decisive Theory for Quantum, ISBN: 979-8-90049-112-7. United Science Press, New York. [19] Arnold VI, Kozlov VV, Neishtadt AI, et al., 2006, Mathematical Aspects of Classical and Celestial Mechanics (Vol. 3, pp. p-XIII). Springer, Berlin.