Code to track coupled orbital-rotational evolution of a planet and satellite
Data files
Sep 05, 2023 version files 8.88 KB
Abstract
The large Kuiper Belt Object Eris is tidally locked to its small companion Dysnomia. Recently obtained bounds on the mass of Dysnomia demonstrate that Eris must be unexpectedly dissipative in order for it to have despun over the age of the solar system. Here we show that Eris must have differentiated into an ice shell and rocky core in order to explain the dissipation. We further demonstrate that Eris's ice shell must be convecting to be sufficiently dissipative, which distinguishes it from Pluto's conductive shell. The difference is likely due to Eris's apparent depletion in volatiles compared with Pluto, perhaps as the result of a more energetic impact.
Methods
This is a code which can be used to reproduce Figs 1 and 2 in the main text.
Figure 1 plots the evolution of the spin and orbital periods of the primary and secondary as a function of distance. It also plots the log of Q/k2 for the primary. Figure 2 plots Q/k2 against the tidal forcing period. The data required to produce these plots are output as a textfile by the code. The caption of Figure 1 reads: "Evolution of Dysnomia’s orbital period and Eris’s spin period. We use the methodology of ref. 21 and assume Eris’s Q varies linearly with forcing frequency. The initial separation is 7Rp and Dysnomia is assumed synchronous throughout, with a mass ratio of 0.084. Crosses are at intervals of 200 Myr. The primary k2 is 0.12 and the Q is 760 for a forcing period of 165 h. Other parameter values are given in Table 1."
Usage notes
It runs on Fortran 77 and produces output (a text file) which can be graphed with commercially-available packages.