- 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).
- 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.
- 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.
- 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
any
Laplace resonance effect.
- The animation gives the exact
1:2:4 Laplace resonance
for illustrative reasons.
You can see the 1:2:4 ratio if you concentrate on 2
of the Galilean moons at once.
- 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.