1 / 2 Θ 3/2 and 1 / 2 Θ 2 resonances can pump Ganymede's free eccentricity up to Θ10 Ψ3 independent of Q Gany /Q J . We also We use the numerical model of R. Malhotra (1991, Icarus show that Ganymede's free eccentricity cannot have been 94, 399-412) to explore the orbital history of Io, Europa, and produced by impact with a large asteroid or comet. Β© 1997 Aca- Ganymede for a large range of parameters and initial conditions demic Press 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 reso-1. INTRODUCTION nance, the Io-Europa conjunction drifts at a mean angular velocity 1 Ο΅ 2n 2 Ψ n 1 , while the Europa-Ganymede conjunc-
The orbital resonances among the jovian moons Io, Eution drifts at a rate 2 Ο΅ 2n 3 Ψ n 2 , where n 1 , n 2 , and n 3 are ropa, and Ganymede present a fascinating dynamical systhe mean motions of Io, Europa, and Ganymede. We find that tem. The strongest resonant interactions are those between Laplace-like resonances characterized by 1 / 2 Θ 3/2 and 1 / Io and Europa and between Europa and Ganymede. The 2 Θ 2 can pump Ganymede's eccentricity to Θ0.07, producing ratios of mean motions (i.e., mean orbital angular velocitidal heating several hundred times higher than at the present ties) of these satellite pairs are both near 2:1, causing their epoch and 2 to 30 times greater than that occurring in the 1 / successive conjunctions to occur near the same jovicentric 2 Θ 1/2 resonance identified previously by Malhotra. The longitude. This allows their mutual gravitational perturbaevolution of 1 and 2 prior to capture is strongly affected by tions to add constructively and, as we shall see later, allows
(Here, Q β«Ψβ¬ Q/k is the ratio of the tidal dissipation a secular transfer of energy and angular momentum from function to second-degree Love number; the subscript J is for Io to Europa to Ganymede. Jupiter.) We find that capture into 1 / 2 Θ 3/2 or 2 occurs over a large range of possible initial satellite orbits if
As the ratio of mean motions is not exactly 2:1, the 4 Ψ 10 Ψ4 , but cannot occur for values Υ 8 Ψ 10 Ψ4 . (The latter conjunctions between Io and Europa drift at a mean anguis approximately two-thirds the value required to maintain Io's lar velocity ΝΆ 1 Ο΅ 2n 2 Οͺ n 1 , while the conjunctions between current eccentricity in steady state.) For constant Q/k, the Europa and Ganymede drift at a rate ΝΆ 2 Ο΅ 2n 3 Οͺ n 2 , where system, once captured, remains trapped in these resonances. n 1 , n 2 , and n 3 are the mean motions of Io, Europa, and We show, however, that they can be disrupted by rapid changes Ganymede. The Io-Europa conjunction is locked to Io's in the tidal dissipation rate in Io or Europa during the course of perijove and also to Europa's apojove; the Europathe evolution; the satellites subsequently evolve into the Laplace Ganymede conjunction occurs when Europa is near periresonance ( 1 β«Ψβ¬ 2 ) with high probability. Because the higher jove. These pairwise resonances are described by the libradissipation in these resonances increases the likelihood of intertion of the following resonance angles: nal activity within Ganymede, we favor the 1 / 2 Θ 3/2 and 2 resonances over 1 / 2 Θ 1/2 for the evolutionary path taken 11 Ο 2 2 Οͺ 1 Οͺ 1 librates about 0Π, by the Galilean satellites before their capture into the Laplace resonance.
12 Ο 2 2 Οͺ 1 Οͺ 2 librates about 180Π,
In addition to its surface appearance, Ganymede's large free 23 Ο 2 3 Οͺ 2 Οͺ 2 librates about 0Π. eccentricity (0.0015) has long been a puzzle. We find that the 93