The steady-state population of Earth's minimoons of lunar provenance

We determine the steady-state population of Earth's minimoons, natural objects temporarily captured in the Earth-Moon system, and quasi-satellites, natural objects on heliocentric orbits with semi-major axes ~1 au that remain close to Earth throughout their orbit, that are derived from lunar ejecta and contrast their orbital distribution and lifetimes with minimoons that evolved out of the main belt as determined by Granvik+ (2012) and Fedorets+ (2017). We do so by tracking the trajectory of synthetic particles launched from the lunar surface at randomly selected locations during the course of the ~19 year Metonic cycle. The particles are launched at a 45° angle relative to the local zenith at evenly spaced azimuthal angles and a range of speeds spanning from the lunar escape speed of 2.38 km s-1 to 4.00 km s-1, faster than the fastest speed at which any particle is ever captured as a minimoon. The particles were tracked until they struck the Moon or Earth or left the 'intermediate source region' (ISR; Granvik+, 2012), the heliocentric orbital element range in which objects may be capturable within the Earth-Moon system. These results were then used to determine the fraction of ejecta that ever become temporarily captured and their average lifetime as minimoons as a function of their ejection speed. We also tracked whether the captures were 'prompt', within the first 10 days after ejection, or 'delayed'. Combining these results with an impactor size-frequency distribution and rate, impactor speed distribution (Marchi+, 2009), the crater scaling relation of Horedt & Neukum (1984), and results of Hirase+ (2004) relating ejecta speed and diameter, allows us to calculate the steady-state number and orbit distribution of Earth's minimoons and quasi-satellites.