434 Encyclopedia of the Solar System
FIGURE 3 Mutual conjunctions resulting from the Laplace resonance of Io, Europa, and
Ganymede. Io completes approximately 4 orbits to every 2 of Europa’s, while Ganymede orbits
approximately once during the same time period. (Left) Mutual conjunction of the
Europa–Ganymede pair. (Right) Io and Europa experience a mutual conjunction one Io day later,
while Europa has moved along half an orbit, and Ganymede has progressed through one-quarter
of its orbit. The resonance forces Europa’s eccentricity to be nonzero, causing tidal heating and
geological consequences.
3.3 Tidal Heating
Europa’s Laplace resonance with siblings Io and Ganymede
causes it to have a slightlyeccentricorbit (e=0.0094).
This eccentricity causes Europa to move closer to and far-
ther from Jupiter (atperijoveandapojove, respectively)
as it moves along its 85 hour orbit, causing the satellite to
undergo increasing and decreasing gravitational pull from
Jupiter. At the same time, Europa undergoeslibrationas
it orbits Jupiter, its tidal bulge necessarily rocking from side
to side as the moon’s orbital velocity changes but the rota-
tion rate stays constant. Europa deforms by∼1–30 m over
each orbital period (Fig. 3), and the dissipation ofstrain
energy resulting from this deformation causes the interior
to warm. Dissipation of tidal energy can happen in several
ways, such as by friction alongfaults, turbulence at liquid–
solid boundaries, andviscoelastic heatingat the scale of
individual ice grains. It is likely that a great degree of tidal
energy is currently dissipated at the base of Europa’s icy
shell, just above the interface between the ice and the un-
derlying liquid ocean, where the ice is warmest and most
deformable on the time scale of the satellite’s orbit. This
regular input of energy is believed to be sufficient to keep
Europa’s ocean liquid.
3.4 Diurnal Stressing
In addition to heating, the tides induced by Europa’s eccen-
tric orbit are believed to be responsible for the majority of its
tectonic processes, including formation of the cracks on its
surface. As Europa orbits, its radial and librational deforma-
tion results indiurnal stresses(so named because Europa’s
day is equal to its orbital period). These stresses are rela-
tively small (=0.1 MPa), but they are apparently sufficient
to crack Europa’s ice shell, producing regions of extensional
and compressional stresses that migrate across the surface,
changing in direction and magnitude as Europa moves
through its eccentric orbit. The magnitude of distortion
and thus stress due to tidal flexing depends on a satellite’s
interior structure. If Europa’s shell were completely frozen,
there would be very little distortion overall, with a tidal am-
plitude of about 1 m, whereas if there is a liquid water ocean
beneath the ice shell, the surface is predicted to distort by
up to 30 m during an orbit. (In comparison, the Earth’s
rocky moon, which has a relatively cold interior, deforms by
∼10 cm over each orbit due to tides raised by the Earth.)
Diurnal stresses have been invoked to explain some of
Europa’s unusual surface features, such as cracks and ridges
(Fig. 4), and likely contribute to the relatively youthful
surface age. Most dramatically, diurnal stresses can explain
the unusualcycloidalshapes of some ridges and bands
on Europa, due to the changing direction and magnitude
of stresses, as further discussed later. Moreover, diurnal
stresses tend to rotate anticlockwise in the northern hemi-
sphere, and clockwise in the southern. These stress rotations
are likely responsible for the observed preponderance of
left-lateralstrike-slipfaults observed in Europa’s north-
ern hemisphere and right-lateral strike-slip faults in the
southern.