Abstract
The paper presents an efficient algorithm for the study of satellite and space debris orbits on long time intervals. The averaged equations of motion are integrated by means of the implicit midpoint method. This approach is known as a symplectic mapping technique. The perturbing forces included in the mapping are: the geopotential, the atmospheric drag, lunisolar perturbations and the direct radiation pressure (without shadow effects). The influence of the atmosphere is approximated by simple methods for the estimation of integrals. The described mapping is valid for the wide range of orbits including the resonant and the eccentric ones; it can be helpful in practical and theoretical problems. The lifetime of GPS transfer orbits is discussed as an exemplary application.
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