How a two-planet smashup left the Earth with its elements

Enlarge / 'No more games, asteroid. Tell us who delivered the stuff! You don't want to upset my partner here...' (credit: NASA)
Imagine reconstructing the itinerary of a globe-trotting, Carmen-Sandiego-like character using nothing but the beach sand accumulated in the bottom of her suitcase. That’s a task that even a CSI writer would consider implausible, but it’s not far off from the work of reconstructing the Earth’s formation.
In the earliest years of the Solar System, matter was clumping together from a diffuse disk of gas and dust spinning around an infant Sun. As the clumps grew, the largest of them could transform, partitioning elements and minerals between inner cores and outer mantles. Clumps from different areas of the disk formed from different starting elements, and collisions mixed this with that. From that chaotic picture, we somehow want to work out how the Earth got the exact mix of elements that helped make it what it is today.
The puzzle of how the Earth got its water is perhaps familiar, but this isn’t the only fleeting substance researchers have pondered. Carbon, nitrogen, and sulfur were also critical “volatile” elements, meaning that they could easily have been boiled off by impacts. But impacts would have also been needed to deliver these materials to a growing Earth. How could both of those be true?
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