Features:

  1. The 1:2:4 Laplace resonance (which is a special set of gravitational perturbations) forces the orbital periods to be in the ratio 1:2:4 for, respectively, Io (orbital period 1.769 days), Europa (orbital period 3.551 days), and Ganymede (orbital period 7.155 days).

  2. Gravitational perturbations (and maybe other astronomical perturbations) constantly perturb the actual ratio away from the exact 1:2:4 ratio, but the 1:2:4 Laplace resonance is stable meaning that a restoring force (which is the special set of gravitational perturbations of the 1:2:4 Laplace resonance) constantly drive the moon system back toward the exact 1:2:4 ratio.

  3. The actual precisely measured ratio at present is 1:2.007:4.045. So NOT exactly the 1:2:4 ratio as expected due astronomical perturbations, but very close to that ratio.

  4. The outermost Galilean moon Callisto (orbital period 16.69 days which is 9.435 in units of Io's orbital period) has avoided being in a Laplace resonance with the 3 inner Galilean moons.

    Probably in Callisto's case, NON-Laplace-resonance astronomical perturbations overwhelm any Laplace resonance effect.

  5. The plot gives the exact 1:2:4 Laplace resonance for illustrative reasons.

  6. All the Galilean moons are tidally locked to Jupiter.

    Thus, their axial rotational periods are exactly the same length as their orbital periods on average and they always turn nearly the same side to Jupiter.