Extended Data Figure 1 : Semi-analytical model of the lunar tidal evolution.

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

Extended Data Figure 1

Evolution of lunar inclination (a) and obliquity (b) as the Moon evolves from 25RE to 60RE using our semi-analytical model (Methods subsection ‘Damping of lunar inclination by obliquity tides’). Initial inclinations were chosen so that the final lunar inclination was the current value of about 5°, while the obliquity was calculated assuming the Moon was in a Cassini state (jumps between 30RE and 35RE are due to the transitions between Cassini states 1 and 2)18. Love numbers were set at their current values (k2,E = 0.3, k2,M = 0.024)35, and the current lunar shape was assumed. The black and red lines plot the solutions for QM = 10,000 and QM = 38 (current value), respectively, while QE was in the range 33–35 range (it was adjusted so that a semimajor axis of 60RE was reached after 4,500 Myr). The blue line plots a history assuming QM = 100 interior to 40RE, and QM = 38 after the Moon passes that distance. The black line closely resembles the results of studies11,12 that neglected lunar obliquity tides, while the other two curves indicate that the past lunar inclination must have been much larger owing to lunar obliquity tides.