Some of the constraints that must be satisfied by a theory of origin are as follows. The Moon is massive relative to its planet compared to Moons around other bodies in the Solar System. The Earth-Moon system exhibits an unusually large amount of angular momentum. The Moon is depleted in volatile elements compared to carbonaceous chondrites which are taken as representative of undifferentiated planetary material. This depletion is taken to indicate that some highly energetic process heated the moon. In contrast, rarefactory elements, such as Ca, Al, Ti, Ba, Sr,..., are enhanced. Iron is depleted relative to its abundance in the earth. The oxygen isotope compositions for the earth and Moon are similar, a fact that suggests that they were formed from the same material and their relative values compared to other bodies in the Solar System suggests that they were formed in the same vicinity.
A major problem with single-impact scenarios is that a single impact cannot provide the observed angular momentum. Rufu et al. argue that the largest impactor is also not necessarily the last one, and that multiple impacts are needed to provide both the observed angular momentum and observed mass.
Rufu et al. point out that computer simulations of impacts show that the projectile contributes more than 70% the the mass of the Earth-orbiting disk in which the ejecta land to later accrete into a single Moon. This so-called "skewed mass" contribution of the impactor is a problem because it is unlikely that the impactor and the proto-earth would have the same composition. How can the Earth and Moon be isotopically similar in oxygen, titanium, tungsten?? In the multi-impact scenario proposed by these authors the proto-Earth experiences a number of collisions by bodies ranging in mass from 0.01 to 0.1 times the mass of the proto-Earth as shown in this figure from the paper:
|Multi-impact scenario for|
Using computer simulations of multiple impacts in which parameters for the impactor mass ratio, speed, direction angle, and planetary rotation were varied, they examined whether or not the earth gained or lost material due to the impact. They found that lower impact angles favored planetary erosion over planetary accretion for the earth. They also found that it was difficult to make a Moon of the current mass from an impact, and that it was easier to create a number of sub-lunar mass disks sequentially, from which the Moon formed by the merger of multiple moonlets as shown in the figure.