<![CDATA[General Background: Orbital elements constitute the fundamental framework for describing and predicting the motion of natural and artificial celestial bodies in celestial mechanics and astrophysics. Specific Background: While classical Keplerian elements adequately represent ideal two-body motion, real orbital dynamics are influenced by gravitational perturbations, non-conservative forces, numerical propagation requirements, and emerging data-driven techniques. Knowledge Gap: A coherent synthesis that integrates classical perturbation theory, advanced numerical methods, and recent machine learning applications across both astrodynamics and astrophysical contexts remains limited. Aims: This review aims to systematically examine the development, theoretical foundations, perturbative evolution, computational propagation methods, and modern AI-assisted approaches to orbital element analysis. Results: The review demonstrates that combining analytical theory with high-fidelity numerical and machine learning models improves orbit prediction accuracy and robustness. Novelty: It provides an integrated perspective linking traditional celestial mechanics with contemporary AI-based methodologies. Implications: The findings support enhanced orbit determination, space situational awareness, and astrophysical modeling of satellites, exoplanets, and small bodies.Keywords : Orbital Elements, Celestial Mechanics, Perturbation Theory, Machine Learning Orbit Prediction, Astrophysical DynamicsHighlight : Perturbations from non-spherical gravity, third-body effects, and drag significantly alter orbital dynamics. Machine learning enhances orbit prediction accuracy, especially for sparse observations and disturbed trajectories. Proper elements enable long-term stability analysis for asteroids and co-orbital body classification.]]>
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