This is an image of Jupiter’s moon Europa taken by the Galileo spacecraft in 1998.
You’ve probably noticed that Europa’s surface, which is made of ice, has tons and
tons of cracks, but I want to direct your attention to this weird repeating arc pattern
– each segment of arc is roughly 100km long!
And there are a lot of these arc patterns.
Most of them are ridges raised up above the surrounding surface, though a few are troughs.
After they were discovered, their shape reminded scientists of a mathematical curve called
a cycloid ; so the Europa curves are called “cycloid curves”.
These curves are weird – geological and astrophysical processes are really good at
making round features, or straight features, or wavy features – but what causes repeated
Well, we think that the Europan surface is made of frozen water at least several miles
thick, which we believe is floating on top of an ocean of liquid water.
This means its surface kind of works the way tectonic plates do here on earth, spreading
apart and generating new ice, crashing together and being subducted, and so on – and here
on earth, plate tectonics has caused cycloid-esque curves all around the pacific ring of fire.
Our best guess for how the pacific arcs form is based on what happens when the ocean plates
get pushed under continental plates: because the earth’s surface is curved, you get a
similar effect to what happens when you dent a ping pong ball – you might get a circle,
or if you press harder, multiple circular arcs: cycloid curves!
However, this doesn’t appear to be the answer on Europa, because there are so many cycloid
curves and they overlap in tons of places and none of them really show signs of one
piece of the surface being pushed under another.
The current best theory for the origin of the Europan cycloids has to do with its weird
Jupiter causes tides on Europa, but they’re not from rotation beneath a tidal bulge (the
way tides are here on earth); the same side of Europa always faces Jupiter.
No, Europa has tides because its orbit isn’t a perfect circle – it’s ever so slightly
elliptical, so as Europa moves closer or farther from Jupiter, the nature of Jupiter’s gravitational
On the scale of the whole moon, these tides manifest as a kind of squeezing and stretching,
which due to the interaction of geometry and physics results in any given point on the
icy surface being pressed together at one time in the orbit, and then stretched at a
And the aspect of tides key to understanding the cycloid curves is that the direction of
the compression and stretching changes over the course of each orbit, rotating around
and around like a hand on a clock.
Specifically, the compression/tension direction rotates clockwise in the southern hemisphere
and counterclockwise in the northern hemisphere, and it takes one orbit to complete a full
So, when there’s enough stretching tension to form a crack in the ice, the crack will
start propagating perpendicular to the tension.
But remember, the direction of the tension is changing.
If, say the crack is growing to the east in the northern hemisphere, the counterclockwise-changing
tension will curve it up away from the equator (and if it’s going west, it’ll curve down
towards the equator).
As Europa continues orbiting, the tension will eventually turn to compression, so the
crack will stop growing.
The compression angle will continue turning, though, and by the time the compression turns
back to tension, the direction will have rotated back around enough that the crack will make
a sharp turn when it starts cracking again.
At which point it resumes its upwards-curving trajectory.
There’s probably a little more subtlety due to a stress-strain process called “tailcracking”
that helps the sharp corners form for each new segment, but this is basically the best
current theory explaining the Europan cycloids: cracks grow because the tides from Jupiter
create tension in the ice, and that tension direction changes over time, curving the crack.
Then the process repeats again, starting the crack off in the original direction, curving
again, and so on.
And that’s how waves form on a frozen world.
This video was supported by NASA’s James Webb Space Telescope Project at the Space
Telescope Science Institute.
There’s still a ton we don’t know about Europa - the Hubble telescope has detected
what we think are plumes jetting from Europa’s surface - perhaps water spouting up through
cracks in Europa’s icy surface, and if so, the plumes could give us insights into the
The James Webb telescope will use its powerful thermal imaging and spectroscopy to investigate
Europa’s plumes and to study the geologic activity, tides, and tectonics of Europa and
other outer solar system planets and moons, hopefully answering questions about how they
formed, how they continue to behave, and whether they have conditions amenable to life.