An efficient algorithm for orbital evolution of artificial satellite

Searching for an accurate model to evaluate the orbital position of the operating satellites and space debris is very important at the time being. This is actually to design different maneuvering schemes to avoid catastrophic consequences of collision. In the present paper a second order theory of perturbations (in the sense of the Hori–Lie perturbation method) is developed. The most dominating perturbations, namely geopotential effects, luni-solar perturbations, solar radiation pressure and atmospheric drag are included. Resonance and very long period perturbations are modeled with the use of semi-secular terms for short time span predictions. A comparison of our analytical solution with a numerical integration (Burlich–Stoer) of the equations of motion for chosen artificial satellites at (LEO, MEO, GEO) is presented. The computations are carried out for different satellite with different area-to-mass ratios showing a good accuracy of the theory.