Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

Optical observations have identified a population of faint objects, with mean motions of about 1 revolution per day and orbital eccentricities as high as 0.6. This discovery was quite surprising, but an explanation was immediately proposed. In fact, direct solar radiation pressure may significantly affect the eccentricity, but not the semi-major axis or mean motion, of objects released into geosynchronous orbits, provided that they are characterized by sufficiently high area-to-mass ratios (A/M). In the meantime, extended analyses and simulations carried out by various authors, coupled with improved telescopic follow-up observations, have shown that objects with extremely high A/M - up to 20-30 m2/kg - are needed to account for the above mentioned debris population and its orbital evolution. It was also shown that below a certain A/M threshold (about 37 m2/kg) the orbits obtained are quite stable, with a lifetime exceeding several decades, while above 40-45 m2/kg, the exact value depending on the initial conditions, the lifetime drops rapidly to a few months. The purpose of this presentation is to describe the results of a similar study focused on the orbits used by the Global Positioning System (GPS). In the simulations carried out, fictitious high A/M objects were released, with a negligible velocity increment, in each of the six orbital planes used by this satellite constellation, in order to investigate their dynamical evolution up to 100 years. The trajectories were propagated taking into account geopotential harmonics, up to 16th degree and order, luni-solar attraction and direct solar radiation pressure, including the eclipses due to the Earth's shadow. In case of induced high eccentricity orbits with perigee altitude below 1000 km, the perturbing effects of air drag were considered as well, adopting the 1976 United States Standard Atmosphere. Even in this case it was found that long lifetime orbits, with mean motions of about 2 revolutions per day, are possible for debris characterized by an extremely high area-to-mass ratio. In general, the lifetime exceeds 100 years up to 45 m2/kg, dropping rapidly to a few months above such A/M threshold, but the evolution depends on the initial conditions, so specific exceptions are possible. If produced, objects like those discovered in synchronous orbits, with A/M as high as 20-30 m2/kg, may survive in this orbital regime as well, with semi-major axes close to the nominal GPS values, maximum eccentricities typically between 0.3 and 0.6, and significant orbit pole precessions (faster and wider for growing A/M values), leading to inclinations between 35 and 90 degrees.