The steady-state population of Earth ’s co-orbitals of lunar provenance

The population of natural objects in a 1:1 mean motion resonance with Earth are known as Earth's co-orbitals. Main belt objects can dynamically evolve into Earth co-orbitals but taxonomic studies of some of them have suggested that they are more likely to be lunar material. While it has long been known that lunar ejecta can achieve Earth co-orbital status, in this work we calculate their expected steady-state size-frequency distribution from the impact rate of asteroids and comets on the Moon's surface, the ejecta's size-frequency and speed distribution, and dynamical integration of the particles for millions of years, among other factors. We also classify known and synthetic co-orbitals by their regime (quasi-satellite, horseshoe, tadpole, or compound) and compute the probability of transitions between them. Our nominal solution predicts that there are $\gtrsim 70$ Earth co-orbitals in the steady-state population larger than $10$ m in diameter with a lunar provenance but there are orders-of-magnitude systematic uncertainty on the value. We used NEOMOD3 to calculate that about 1600 are expected in the co-orbital population with a main belt provenance and they have higher eccentricity and inclination than those from the Moon. New taxonomic classifications for more Earth co-orbitals will reduce the uncertainties on e.g. crater scaling relations that will, in turn, reduce the uncertainties in the calculation of the steady-state population of Earth's co-orbitals with a lunar origin. The mineralogy and abundance of Earth's co-orbitals is also of interest to commercial asteroid mining ventures because they are the lowest $Δv$ targets in the asteroid population.