Extended Data Figure 8: Simple physical models for reorienting the Moon, and the effect of lunar impact basins.

a, A schematic of our spherical cap model, showing a spherical cap on the surface of the Moon (green circle), centred on a particular latitude and longitude (arrow). b, The mass anomaly ΔQ for a spherical cap as a function of cap size and cap surface density (or cap thickness, assuming a density of ρ = 2,550 kg m⁻³). c, A schematic of our mantle-spanning interior anomaly, with a spherical mass anomaly (green circle), centred on a particular latitude and longitude (arrow), grazing the core (dark grey circle) and the surface. d, The mass anomaly ΔQ for the spherical mantle anomaly as a function of the density contrast of the anomaly (black line). Over-plotted (green shading and orange lines) is the ΔQ required if the PKT is responsible (ΔQ = −0.45; Fig. 3c). e, North polar projection of all possible palaeopole positions based on a mass anomaly placed at either the PKT or South Pole–Aitken basin (SPA). PKT paths always pass through the neutron palaeopole, whereas SPA paths are nearly orthogonal to this path. f, Mass anomalies ΔQ of the largest lunar impact basins derived from inverse fitting of the present-day lunar gravity field, following the method outlined in ref. 21. The only impact basin with a large enough mass anomaly is the South Pole–Aitken basin, which is not properly located to drive the observed TPW (Fig. 3b). The only major impact basin that is properly located is Moscoviense, which has a negligible mass anomaly (and with the wrong sign). Error bars are 1σ uncertainties from the inverse solution (see ref. 21).