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. Author manuscript; available in PMC: 2019 Oct 1.
Published in final edited form as: Nat Astron. 2019 Apr 1;3:543–552. doi: 10.1038/s41550-019-0726-y

Figure 1. Evolution of the moons’ semi-major axes over time due to tidal dissipation inside Saturn.

Figure 1.

The color-coding for each moon is indicated by moon initials (R=Rhea, D=Dione, T=Tethys, E=Enceladus, M=Mimas) to the right of panel (e). Tides result in transfer of angular momentum from fast-spinning Saturn into the moons’ orbits, increasing semi-major axes at a rate inversely proportional to the tidal Q of Saturn (second term in equation 4). Semi-major axes are shown as a function of time for five initial values of Saturn’s Q, all decreasing linearly to 2452.8 at the present day. These simplified models are used to determine appropriate starting moon semi-major axes or formation times for each starting Q. These are not fully accurate because moon-moon and moon-ring interactions are neglected; so is tidal dissipation inside the moons. Accounting for interactions between Enceladus and the present-day ring would result in minimum initial Q ≿ 80000 (rather than Q ≿ 50000; panel c) for Enceladus to be primordial. The curves are overlain on color bands depicting Saturn and its rings. Major mean-motion resonances (j: j + k for j ≤ 5 and k ≤ 3) are indicated; those already present in panels to the left are grayed out and not all named.