Planar near-Earth asteroids in resonance with the Earth

In this paper, we investigate planar near-Earth asteroids (NEAs) in resonance with the Earth. Integrable approximations for both prograde and retrograde two-body mean motion resonances (MMRs) are introduced in the planar circular restricted three-body problem (CRTBP). A preliminary analysis is implemented in the CRTBP to select candidate planar resonant NEAs. Based on limitations on the inclinations and semimajor axes, 510 candidate resonant NEAs are obtained. We propose a parameter to measure the minimum distance of the trajectory from the collision curve in the CRTBP. The obtained candidate resonant NEAs are further investigated in the ephemeris model, where the gravities of the nine planets are considered and the initial states of the nine planets are obtained from the Jet Propulsion Laboratory (JPL) database. Encounter times are defined as the time intervals between two successive encounters and are recorded through numerical integration. Among 510 candidate resonant NEAs, 386 Earth-crossing NEAs with encounter times smaller than 10,000 years are analyzed in detail. NEAs with distances from the nearest neighboring resonance below 0.015 au are defined as compact NEAs, while those with distances above 0.015 au are defined as sparse NEAs. Numerical tests indicate that compact NEAs have a weak correlation between the minimum distance to the collision curve and the encounter time, but sparse NEAs, whether with or without other planets' encounters have a strong linear correlation between the minimum distance to the collision curve and the encounter time in a statistical sense. Depending on the value of the minimum distance to the collision curve, Earth-crossing NEAs are classified into resonant and nonresonant NEAs in the CRTBP. Numerical results show that a resonant NEA in the CRTBP is more likely to have a larger encounter time in the ephemeris model than a nonresonant NEA in the CRTBP, especially for sparse NEAs. Finally, three resonant sparse NEAs and three compact NEAs are demonstrated in detail.