Analysis of orbital perturbations acting on objects in orbits near geosynchronous Earth orbit

Abstract

Orbital evolution has been numerically simulated for objects started in geosynchronous Earth orbit (GEO) or in orbits near GEO, during a project to study potential orbital debris problems in this region. Perturbations simulated include nonspherical terms in the Earth's geopotential field, lunar and solar gravity, and solar radiation pressure. Objects simulated include large satellites, for which solar radiation pressure is insignificant, and small particles (a few microns in diameter), for which solar radiation pressure is an important force. Results for large satellites are largely in agreement with previous GEO studies that used classical perturbation techniques; orbital evolution studies were extended to possible storage orbits slightly above or below GEO. One notes that while the orbit planes of GEO satellites initially placed in equatorial orbits precess, so that those orbits reach inclinations of 14° to 15° to the equator, a “stable plane” exists inclined approximately 7.3° to the equator. The orbit planes of GEO satellites placed in such a stable plane orbit experience very little precession, remaining always within 1.2° of their initial orientation. Solar radiation pressure generates two major effects on small particles. One is an orbital eccentricity oscillation anticipated from previous research. The other is an oscillation in orbital inclination. This orbital inclination pattern is due to a precession of the small particle's orbital angular momentum vector about an axis offset from the Earth's polar axis. The magnitude of the precession axis offset angle depends on the particle's cross‐sectional area to mass ratio. The rate for this precession differs greatly from the precession rate predicted in a previous study using perturbation techniques. This difference points up the inadequacy of those perturbation techniques for orbits with large eccentricities. For one sequence of runs with small particles, Poynting‐Robertson drag was added to the simulation in order to slowly reduce the orbital semimajor axis and probe for possible orbital period resonances near the GEO distance. A significant resonance was found at the geosynchronous distance, where small grains are trapped into a 1:1 resonance with the Earth's daily rotation.