Extended Data Figure 2 : Lunar tidal evolution following planetesimal encounters.

From: Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Extended Data Figure 2

Evolution of lunar inclination (a) and eccentricity (b) following the excitation of the lunar inclination by encounters with planetesimals as proposed by ref. 3, using our semi-analytical model. The two sets of initial conditions are for the state a = 47RE, i = 5.8° featured in ref. 3 (Fig. 1), and a possible outcome with a more excited inclination i = 10° (also at a = 47RE). The initial eccentricities were estimated as e = 2sini. The black lines show the evolution assuming QM = 38 and QE = 34, with the current Love numbers. The red line plots the evolution for QM = 100 and the blue line the evolution for QE = 20. The circle symbol plots the current inclination and eccentricity of the lunar orbit. No combination of tidal parameters can simultaneously match both the current lunar inclination and eccentricity at the same time. A small QM combined with high e also keeps the Moon from reaching 60RE (top two lines). Decreasing QE also does not help, as stronger Earth tides further increase the lunar eccentricity (blue line).