Tidal evolution into the Laplace resonance and the resurfacing of Ganymede

Adam P. Showman, Renu Malhotra

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


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 ω1 ≡ 2n2 - n1, while the Europa-Ganymede conjunction drifts at a rate ω2 ≡ 2n3 - n2, where n1, n2, and n3 are the mean motions of Io, Europa, and Ganymede. We find that Laplace-like resonances characterized by ω12 ≈ 3/2 and ω1/ ω2 ≈ 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 (ω1/ ω2 ≈ 1/2 resonance identified previously by Malhotra. The evolution of ω1 and ω2 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 ω12 ≈ 3/2 or 2 occurs over a large range of possible initial satellite orbits if Q′Io/Q′J ≤ 4 × 10-4, but cannot occur for values ≥ 8 × 10-4. (The latter is approximately two-thirds the value required to maintain Io's current eccentricity in steady state.) For constant Qlk, 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 (ω1 = ω2) with high probability. Because the higher dissipation in these resonances increases the likelihood of internal activity within Ganymede, we favor the ω12 ≈ 3/2 and 2 resonances over ω12 ≈ 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 ω12 ≈ 3/2 and ω12 ≈ 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.

Original languageEnglish (US)
Pages (from-to)93-111
Number of pages19
Issue number1
StatePublished - May 1997

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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