The steady state population of Earth’s minimoons of lunar provenance

This work examines the plausibility of a lunar origin of natural objects that have a negative total energy with respect to the geocenter, i.e. $E_T=$potential＋ kinetic energy$<0$, while they are within 3 Earth Hill radii ($R_H$), a population that we will refer to as ‘bound’. They are a super-set of the informally named population of ‘minimoons’ which require that the object make at least one orbit around Earth in a synodic frame rotating with Earth and that its geocentric distance be $<R_H$ at some point while $E_T<0$. Bounded objects are also a dynamical subset of the population of Earth’s co-orbital population, objects in a 1:1 mean motion resonance with Earth or, less specifically, on Earth-like orbits. Only two minimoons have been discovered to date, 2006 RH₁₂₀ and 2020 CD${}_3$, while 2024 PT${}_5$ and 2022 NX${}_1$ meet our condition for ’bound’. The likely source region of co-orbital objects is either the MB of asteroids, lunar ejecta, or a combination of both. Earlier works found that dynamical evolution of asteroids from the MB could explain the observed minimoon population, but spectra of 2020 CD${}_3$ and 2024 PT${}_5$ and Earth co-orbital (469219) Kamo‘oalewa are more consistent with lunar basalts than any MB asteroid spectra, suggesting that the ejection and subsequent evolution of material from the Moon’s surface contributes to the minimoon and, more generally, Earth’s co-orbital population. This work numerically calculates the steady-state size-frequency distribution of the bound population given our current understanding of the lunar impact rate, the energy of the impactors, crater-scaling relations, and the relationship between the ejecta mass and speed. We numerically integrate the trajectory of lunar ejecta and calculate the statistics of ‘prompt’ bounding that take place immediately after ejection, and ‘delayed’ bounding that occurs after the objects have spent time on heliocentric orbits. A sub-set of the delayed bound population composes the minimoon population. We find that lunar ejecta can account for the observed population of bound objects but uncertainties in the crater formation and lunar ejecta properties induce a many orders of magnitude range on the predicted population. If the bound objects can be distinguished as lunar or asteroidal in origin based on their spectra it may be possible to constrain crater formation processes and the dynamical and physical evolution of objects from the MB into near-Earth space.