Semianalytic theory of motion for close-Earth spherical satellites including drag and gravitational perturbations

A semianalytic theory for long-term dynamics of a low Earth orbit artificial satellite, or a space debris particle, is presented. The empirical model TD88 of the neutral atmosphere density distribution, simple enough to allow analytic removal of short period perturbations, is the principal part of the theory. In order to compare our results with observations of passive spherical bodies, we also include the main gravitational effects, notably those of the zonal harmonics J 2 , … , J 9 ( J 2 2 terms are also considered), and for low eccentricities and inclinations we use the description in nonsingular elements. Starting with a single set of initial orbital data and giving a certain “confidential interval” on the resulting lifetimes, we find a reasonably good agreement with observations over the timescale of years, the mean computed lifetimes being a few percent apart from the real ones. The strength of our theory is the computational efficiency, since we need only ≃ 5 s (on a PC equipped with Intel Celeron 1.7 GHz) to propagate the 10-year orbital arc, while maintaining a lot of the physics of the motion under drag (solar flux, geomagnetic activity, local time, geographic latitude). The online calculation as well as the code are available on the internet.