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The Moon likely formed from a giant collision between the proto-Earth and a Mars-sized body around 4.5 Ga. This impact explains the Moon's mass, orbital parameters, and the Earth-Moon system's high angular momentum. Isotopic similarities between the Moon and Earth support this origin rather than Earth capture or co-accretion.
The Moon is anomalous. It is far too large relative to its host planet — about 1/81 of Earth's mass — to be a typical captured asteroid, and its orbital properties and composition pose puzzles that simpler formation models cannot resolve. Your understanding of planetary differentiation tells you that by the time of the hypothesized impact (~4.5 billion years ago), the proto-Earth had already separated into an iron core and a silicate mantle. The Moon, strikingly, has a tiny iron core — only about 1–2% of its mass compared to Earth's ~32%. Any formation model must explain this iron depletion, along with the Moon's bulk composition, the angular momentum of the Earth-Moon system, and the near-identical oxygen isotope ratios between Earth and lunar samples.
The giant impact hypothesis proposes that a Mars-sized body — often called Theia — struck the proto-Earth in a glancing collision at roughly 4.5 Ga. Your knowledge of conservation of momentum helps here: a glancing impact transfers enormous angular momentum to the system, explaining why the Earth-Moon system has an unusually high total angular momentum. The collision was energetic enough to partially vaporize both bodies, ejecting a disk of superheated silicate debris into orbit around the proto-Earth. This debris disk, drawn predominantly from the mantles of both Theia and the proto-Earth (since dense iron cores would have merged rather than being launched into orbit), then accreted to form the Moon. This neatly explains why the Moon is iron-poor: the disk material was mostly silicate mantle, not metallic core.
The strongest evidence favoring the giant impact over competing hypotheses — co-accretion (Earth and Moon forming side by side from the same material) and capture (Earth gravitationally snaring a passing body) — comes from isotopic geochemistry. Oxygen isotopes vary measurably between different bodies in the solar system: Mars, meteorite parent bodies, and Earth each have distinct oxygen isotope signatures. Yet lunar samples returned by the Apollo missions have oxygen isotope ratios virtually identical to Earth's. Co-accretion could potentially explain this similarity, but it fails to account for the Moon's iron depletion and the system's angular momentum. Capture would predict a distinctly different isotopic signature. The giant impact, particularly in models where the impactor's material thoroughly mixes with Earth's mantle before the Moon-forming disk condenses, naturally produces isotopic homogeneity.
Modern computational simulations using smoothed particle hydrodynamics (SPH) have refined the hypothesis significantly. Early models required Theia to strike at a specific angle and velocity, and they tended to produce a Moon composed mostly of Theia's material — which would predict isotopic differences from Earth, not similarities. More recent models explore scenarios including a higher-energy impact that completely vaporizes both bodies into a mixed "synestia" (a donut-shaped cloud of rock vapor), or a smaller, faster impactor. These variants better reproduce the observed isotopic similarity by ensuring thorough mixing. The giant impact hypothesis remains the leading model for lunar origin, but the details of the impact geometry and the physics of disk-to-Moon accretion are still active areas of research.