Investigating the Role of Earth's Quasi-Satellite Resonance in the Accretion of Interplanetary Dust

We studied the orbital evolution of low inclination asteroidal interplanetary dust particles (IDPs) decaying towards 1 AU under the influence of radiation pressure, PR drag, and solar wind drag. We used a series of β values (the ratio of radiation pressure to central gravity) ranging from 0.0025 up to 0.02. Assuming a composition consistent with astronomical silicate and a particle density of 2.5 g cm^-3 these β values correspond to diameters ranging from 200 down to 25 microns, respectively. Simulations with the larger IDPs (>50 microns) typically showed that 100% of the dust particles became temporarily trapped in mean-motion resonances outside Earth's orbit. When trapped in these outer resonances a dust particle's orbital eccentricity significantly increases (sometimes to e > 0.2) while its decay in semi-major axis is halted. Most dust particles eventually slip out of these outer resonances and their orbits continue decaying inwards toward 1 AU. We found that a significant fraction of the initial populations subsequently became trapped in 1:1 co-orbital resonance with Earth. In addition to traditional horseshoe type co-orbitals, IDPs also became trapped as so-called quasi-satellites. About 1% of the smallest IDPs (25 microns) and 10% of the largest (200 microns) became trapped in the quasi-satellite resonance for some length of time. Quasi-satellite IDPs always remain relatively near to Earth, within about 0.2-0.3 AU, and undergo two close-encounters with Earth each year. While resonant perturbations from Earth halt the decay in semi-major axis of quasi-satellite IDPs their eccentricities continue to decrease, forcing the IDPs onto more Earth-like orbits and causing them to spiral closer and closer to Earth. This has dramatic consequences for the relative velocity and distance of closest approach between Earth and the IDPs. After about 10⁴ years in the quasi-satellite resonance IDPs are typically less than 0.1 AU from Earth and consistently coming within about 0.03 AU. In the late stages of evolution as IDPs leave the quasi-satellite resonance they can have deep close-encounters with Earth significantly inside the Hill radius (0.01 AU, inside of which Earth's gravity dominates the sun's). As they leave the resonance the effective encounter velocities between these quasi-satellite IDPs and Earth are just a few hundred meters per second, well below the average values of 2-4 km s^-1 for non-resonant asteroidal IDPs with similar initial orbits. This factor alone leads to about a 10-100 fold increase in Earth's effective gravitational cross-section for quasi-satellite IDPs compared to non-resonant IDPs with similar orbital elements, and a factor of 100-1000 or more compared to cometary IDPs. This suggests that even if quasi-satellite dust represents as little as 0.1% of all Earth-crossing dust particles it could still be a significant or perhaps dominant source of IDPs accreted by our planet. Because quasi-satellite resonant trapping is dependent on the host planet's eccentricity, accretion of quasi-satellite IDPs likely varies with Earth's eccentricity on 10⁵ year time scales. [This work is supported by NASA grant NNX10AJ61G.]