Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites

Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term orbits natural and artificial bodies. Using high-order normal constructions, we provide three different orbital point-mass satellites orbiting around Earth. i) We demonstrate long term semimajor axis within framework $J_2$ problem, by construction eliminating fast angle in corresponding Hamiltonian obtaining $H_{J_2}$ . ii) eccentricity inclination secular model including lunisolar perturbations (the 'geolunisolar' $H_{gls}$), after suitable reduction to Laplace plane. iii) numerically examine convexity steepness properties integrable part both $H_{gls}$ models, which reflect necessary conditions holding Nekhoroshev's theorem on exponential orbits. find that is non-convex, but satisfies 'three-jet' condition, while restores quasi-convexity adding terms Hamiltonian's part.