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

Abstract

This work examines the plausibility of a lunar origin of natural objects that have a negative total energy (ET) with respect to the geocenter while within 3 Earth Hill radii (RH), a population that we will refer to as 'bound'. They are a super-set of the 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 <RH at some point while ET<0. Only two minimoons have been discovered to date, 2006 RH120 and 2020 CD3, while 2024 PT5 and 2022 NX1 meet our condition for 'bound'. The likely source region of co-orbital objects is either the main belt, 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 CD3 and 2024 PT5 and Earth co-orbital (469219) Kamo'oalewa are more consistent with lunar basalts than any MB asteroid spectra. This work calculates the steady-state size-frequency distribution of the bound population given our understanding of the lunar impact rate, the energy of the impactors, crater-scaling relations, and the relationship between the ejecta mass and speed. We 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 based on their spectra it may be possible to constrain crater formation processes.