Extended Data Figure 8 : Lunar obliquity close to the Cassini state transition.

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

Extended Data Figure 8

Obliquities for four ‘slices’ in inclination (at 5°, 10°, 15° and 20°) from the grid of short simulations shown in Extended Data Fig. 7 (solid red and magenta lines with points; the obliquities and inclinations are in the same order at far left and far right). When two different simulations for the same a and i differed in outcome, we chose the solution within the Cassini state, if available. The blue dashed lines plot the relevant Cassini states calculated using analytical formulae, while the black dashed line at 58.15° plots the upper limit for stable obliquities in the relevant Cassini state. Although the numerical and analytical results agree at the smallest and largest semimajor axes, the large discrepancies in between are due to non-synchronous rotations being dominant at the Cassini state transition.