Recent progress in analytical orbit theories

Abstract

Numerical integration of equations of motion is commonly used when a very high accuracy of an artificial satellite trajectory description is needed for a small number of the Earth's or a planet's orbiters. However for a large number of satellite orbits, which have to be determined simultaneously (e.g. in the problem of a collision avoidance between operating satellites and space debris) numerical integration is costly in terms of computer time, and the analytical methods became advantageous. Qualitative analysis of a satellite motion also needs an application of analytical formulas that describe the motion. Thus the development of analytical theories is still a task of great importance. Since the late 1950's, when the first satellite theories were developed by Brouwer, Kozai, Garfinkel and others, great progress has been achieved in the modeling of artificial satellite motion. New perturbation methods as well as new analytical theories have been developed. The theories include secular, long- and short-period perturbations of the first order due to arbitrary geopotential coefficients and perturbations of the higher order due to selected coefficients (in particular low zonal harmonic coefficients). Great progress has been achieved in semi-numerical and semi-analytical theories. Several solutions concern special types of orbits (e.g. orbits at the critical inclination, frozen orbits, resonance orbits). This paper presents a review of contemporary theories of artificial satellite motion and recent developments in this area. Since it is impossible to include all important and significant works, only selected results are presented.