Mathematics – Probability
Scientific paper
May 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997icar..127...93s&link_type=abstract
Icarus, Volume 127, Issue 1, pp. 93-111.
Mathematics
Probability
52
Scientific paper
We use the numerical model of R. Malhotra (1991, Icarus 94, 399-412) to explore the orbital history of Io, Europa, and Ganymede for a large range of parameters and initial conditions near the Laplace resonance. We identify two new Laplace-like resonances which pump Ganymede's eccentricity and may help explain the resurfacing of Ganymede. Near the Laplace resonance, the Io-Europa conjunction drifts at a mean angular velocity omega_1 = 2n_2 - n_1, while the Europa-Ganymede conjunction drifts at a rate omega_2 = 2n_3 - n_2, where n_1, n_2, and n_3 are the mean motions of Io, Europa, and Ganymede. We find that Laplace-like resonances characterized by omega_1/omega_2 ~ 3/2 and omega_1/omega_2 ~ 2 can pump Ganymede's eccentricity to ~0.07, producing tidal heating several hundred times higher than at the present epoch and 2 to 30 times greater than that occurring in the omega_1/omega_2 ~ 1/2 resonance identified previously by Malhotra. The evolution of omega_1 and omega_2 prior to capture is strongly affected by Q'_Io/Q'_J. (Here, Q' = Q/k is the ratio of the tidal dissipation function to second-degree Love number; the subscript J is for Jupiter.) We find that capture into omega_1/omega_2 ~ 3/2 or 2 occurs over a large range of possible initial satellite orbits if Q'_Io/Q'_J <= 4 x 10^-4, but cannot occur for values >= 8 x 10^-4. (The latter is approximately two-thirds the value required to maintain Io's current eccentricity in steady state.) For constant Q/k, the system, once captured, remains trapped in these resonances. We show, however, that they can be disrupted by rapid changes in the tidal dissipation rate in Io or Europa during the course of the evolution; the satellites subsequently evolve into the Laplace resonance (omega_1 = omega_2) with high probability. Because the higher dissipation in these resonances increases the likelihood of internal activity within Ganymede, we favor the omega_1/omega_2 ~ 3/2 and 2 resonances over omega_1/omega_2 ~ 1/2 for the evolutionary path taken by the Galilean satellites before their capture into the Laplace resonance. In addition to its surface appearance, Ganymede's large free eccentricity (0.0015) has long been a puzzle. We find that the omega_1/omega_2 ~ 3/2 and omega_1/omega_2 ~ 2 resonances can pump Ganymede's free eccentricity up to ~10^-3 independent of Q'_Gany/Q'_J. We also show that Ganymede's free eccentricity cannot have been produced by impact with a large asteroid or comet.
Malhotra Renu
Showman Adam P.
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