The 'fast-spinning Earth' scenario, proposed by Ćuk and Stewart9, invokes the collision of an object slightly smaller than Mars with an Earth that is already rotating with a 2–2.5-hour day owing to a previous large impact. Because Earth is spinning close to the critical rate at which it becomes unstable, the Moon-forming impact ejects part of Earth's mantle into orbit, leading to a disk.
Also in 2012, I proposed the 'half-Earth impactor' scenario10. Here, the Moon arises from a collision between two planets, each of about half of Earth's mass (see 'How to make a Moon'). Both final planet and disk then comprise about half impactor and half target material. This model is simpler than the fast-spinning-Earth model because it does not require a specific prior large impact. But it demands a large impactor, and so may still be less probable than the canonical impact.
Both 2012 models account for the similar oxygen, chromium and titanium compositions of the Moon and Earth. To explain similarities in silicon and tungsten — elements that interact with metals — both models require that the impactor's iron core remains largely intact as it descends through Earth's mantle to merge with Earth's core, avoiding substantial metal–silicate interactions. But it remains unclear whether the resonance mechanism needed to slow Earth's rotation in these more extreme scenarios is likely or requires an improbably narrow range of conditions. In other words, is the origin of our Moon a rarer event than we believed, or are we missing something?