Mathematical analysis of orbital mechanics with perturbation methods

Orbital mechanics with perturbation methods gives us a way to look at departures from the idealized Keplerian motion using math. Changes happen because of gravity, uneven mass distributions, air drag, sun radiation pressure, and relativistic corrections. This research looks into mathematical and numerical perturbation methods, focusing on how well they can predict orbital paths and long-term stability. Numerical methods let us directly integrate complex dynamical systems, while analytical methods give closed-form answers for simple changes. A comparison analysis shows the pros, cons, and areas where each one can be used. The study shows that perturbation methods are very important for current astrodynamics, satellite tracking, and mission planning in settings with many bodies.