M.L. Lidov (1962)
Classic (original!) paper deriving simple secular formulas for third-body perturbations that predict large eccentricity swings in high satellite orbits.
Lidov develops compact analytic formulas to approximate how a planet’s satellite orbit evolves under gravitational perturbations from external bodies (e.g., Moon/Sun), avoiding costly full numerical integration. Using expansions in the small ratio of satellite distance to perturber distance and averaging over orbital periods, he derives secular (long-term) evolution equations and identifies strong, geometry-dependent changes in eccentricity and inclination that can drive perigee up or down dramatically. The paper also gives practical computation recipes (step-by-step difference equations) and validates accuracy against direct numerical integrations for challenging Earth- and Moon-satellite cases. These results helped establish the dynamical mechanism later widely known as the Lidov–Kozai effect and remain central for predicting stability and lifetime of high-altitude satellites and other hierarchical three-body systems.
Analytic perturbation theory with series expansion of third-body forces and averaging over the satellite and perturber orbital periods, plus numerical cross-checks.
Celestial mechanics basics (orbital elements, perturbation/averaging methods) and familiarity with third-body gravitational effects.
A fundamental analytical work revealing the Lidov–Kozai effect in the dynamics of satellites
— ES