  The Earth-Moon system is suggested to have formed through a single giant
collision, in which the Moon accreted from the impact-generated debris disk.
However, such giant impacts are rare, and during its evolution the Earth
experienced many more smaller impacts, producing smaller satellites that
potentially coevolved. In the multiple-impact hypothesis of lunar formation,
the current Moon was produced from the mergers of several smaller satellites
(moonlets), each formed from debris disks produced by successive large impacts.
In the Myrs between impacts, a pre-existing moonlet tidally evolves outward
until a subsequent impact forms a new moonlet, at which point both moonlets
will tidally evolve until a merger or system disruption. In this work, we
examine the likelihood that pre-existing moonlets survive subsequent impact
events, and explore the dynamics of Earth-moonlet systems that contain two
moonlets generated Myrs apart. We demonstrate that pre-existing moonlets can
tidally migrate outward, remain stable during subsequent impacts, and later
merge with newly created moonlets (or re-collide with the Earth). Formation of
the Moon from the mergers of several moonlets could therefore be a natural
byproduct of the Earth's growth through multiple impacts. More generally, we
examine the likelihood and consequences of Earth having prior moons, and find
that the stability of moonlets against disruption by subsequent impacts implies
that several large impacts could post-date Moon formation.
