By splitting this process into two phases, it is the first model to account for some crucial differences between Moon and Earth rocks.
The work appears in Nature Geoscience.
Rich filling
In general, the Earth and Moon are remarkably alike in their mineral make-up. This has led scientists to propose that the smash-up that eventually spawned the Moon was caused by a Mars-sized interloper made of surprisingly similar stuff to Earth.
But there are some noteworthy differences, which Moon origin models have struggled to account for.
"One of the key differences, that`s been known since the Apollo sample return, is that the Moon is much more depleted in so-called volatile elements - those that vaporise easily as you heat up material," said Dr Robin Canup, the new study`s lead author, from the Southwest Research Institute in Colorado, US.
"And the origin of this depletion has been essentially unknown."
These volatile elements, it is worth noting, are not things we think of as wet and wispy here on Earth; Dr Canup and her colleagues were looking primarily at metals like zinc, potassium and sodium - which are volatile in the context of Solar System formation.
To address the problem of the Moon`s missing volatiles, Dr Canup`s team added temperature and chemical models to a framework they had already developed for the physical dynamics of how the Moon assembled from the magma disc.
In the very first months and years after the collision, about half the Moon`s mass was crunched into a ball at the fringe of the disc, which at that stage surrounded the fledgling Earth like Saturn`s rings. Because this early material came from the edge of the rings, it was cool and contained a good mix of volatile elements.
But subsequently, the outer half of the Moon was formed by molten material slapping on to the expanding satellite from the inner portion of the disc.
This stuff, according to Dr Canup`s new model, was too hot for volatile elements to condense with it. So the Moon`s outer layers - where all the rocks we`ve sampled come from - ended up "volatile-poor".
"What we find," she told the BBC, "is that the initial half of the Moon, say 50% of its mass, may well have retained its volatile species. But for the last half, as that material accreted on to the Moon, it was consistently too hot to contain the volatile species."
After accumulating these two layers, the model suggests that the Moon swung further away from the Earth. This is a key aspect of the findings, Dr Canup explained, because it locks the discrepancy in place.
"The Moon`s orbit expands enough to turn off its accretion, before the inner disc gets cool enough for the volatiles to condense.
"So by the time they do condense, they`re scattered on to the Earth rather than swept up by the Moon."
Missing pieces
Dr Mahesh Anand, a planetary scientist at the Open University in the UK, said the research was "very elegant" and thorough, and offered an excellent match for some - but not all - measurements of lunar chemistry.
"It is a good way of explaining a Moon that is volatile depleted," he told BBC News. "But I also feel that you need a number of other processes to have affected these volatiles afterwards - before the Moon completely solidified - in order to reconcile all of the observations that we are making in the laboratory."
For example, Dr Anand said, there are discrepancies in the isotopes of zinc found in Earth and Moon rock, as well as the question of how much water there is - and was - on the Moon.
"But until now, nobody had tried to build so many aspects into one model," he said.
In a commentary for Nature Geoscience, Prof Steve Desch from Arizona State University said this latest view of the Moon`s origin was one of the most complete yet.
"No other model of the Moon`s formation is as comprehensive, or is as capable of making such detailed predictions about the Moon`s composition," he wrote.
Prof Desch also compared the new Moon model to Chinese "mooncakes" or yue bing, traditionally baked for an Autumn festival. These cakes have a moist filling baked inside a dry pastry.
Just like these cakes, he suggested, the Moon may have required a "two-step recipe".
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