  According to the generally accepted scenario, the last giant impact on the
Earth formed the Moon and initiated the final phase of core formation by
melting the Earth's mantle. A key goal of geochemistry is to date this event,
but different ages have been proposed. Some argue for an early Moon-forming
event, approximately 30 million years (Myr) after the condensation of the first
solids in the Solar System, whereas others claim a date later than 50 Myr (and
possibly as late as around 100 My) after condensation. Here we show that a
Moon-forming event at 40 Myr after condensation, or earlier, is ruled out at a
99.9 per cent confidence level. We use a large number of N-body simulations to
demonstrate a relationship between the time of the last giant impact on an
Earth-like planet and the amount of mass subsequently added during the era
known as Late Accretion. As the last giant impact is delayed, the late-accreted
mass decreases in a predictable fashion. This relationship exists within both
the classical scenario and the Grand Tack scenario of terrestrial planet
formation, and it holds across a wide range of disk conditions. The
concentration of highly siderophile elements (HSEs) in Earth's mantle
constrains the mass of chondritic material added to Earth during Late
Accretion. Using HSE abundance measurements, we determine a Moon-formation age
of 95 +/- 32 Myr since condensation. The possibility exists that some late
projectiles were differentiated and left an incomplete HSE record in Earth's
mantle. Even in this case, various isotopic constraints strongly suggest that
the late-accreted mass did not exceed 1 per cent of Earth's mass, and so the
HSE clock still robustly limits the timing of the Moon-forming event to
significantly later than 40 My after condensation.
