More on the invisible oceans, and their roundness

Previously, in speculating about what it would take for an inhabitant of one of the several subsurface oceans thought to exist in our solar system to discover that their world was round, I said

Figuring out that the world is round would be a significant accomplishment.  The major cues the Greeks used -- ships sinking below the horizon, lunar eclipses, the position of the noontime sun at different latitudes -- would not be available.  The most obvious route left is to actually circumnavigate the world.  And figure out that you did it.

Fortunately, I was smart enough to leave myself some wiggle room: "I'm very reluctant to say 'such and such would be impossible because ...'"  After all, humanity is in a similar situation in trying to figure out the shape of our universe, though in our case circumnavigating doesn't seem to be even remotely close to an option.  Even so, we've had some apparent success.

On further reflection, there are at least two ways an intelligent species living in a world like Ganymede's subsurface ocean could figure out that the world is round.

First, and perhaps most likely, it's not necessary for a Ganymedean to circumnavigate the world, if something can.  In this case that something would be sound.  Under the right conditions, sound can travel thousands of kilometers underwater.  The circumference of Ganymede is around 10,000km, which may be too far.  Europa's is around 6,000km, which as I understand it is on the edge of what experiments in Earth's oceans have been able to detect (pretty impressive, that).

We've already postulated that sound would be one of the more important senses in such a world.  It doesn't seem impossible that someone would notice that especially loud noises tended to be followed a couple of hours later by similar noises from all directions.  This assumes that the the oceans are unobstructed, but if they're not, you have landmarks to measure by, which would make the original "circumnavigate and tell that you did it" less of a challenge.

Second, if some sort of light-production and light-detection evolve, then one of the cues the Greeks used is indeed available, at least in theory: one can see things disappear over the horizon.  To actually make use of this one would need to be able to see far enough to tell that the object was disappearing due to curvature and not behind some obstacle, or simply because it was too far away to see.  The exact details depend on how smooth the inner surface is.

Humans noticed the effect with ships because a calm sea is quite flat, that is to say, quite close to perfectly round.  If the inner surface of the ocean is rough, one might have to float at a considerable distance from it, and thus wait for the object to recede a considerable distance, to be sure of the effect.  On the other hand, floating a considerable distance from the inner surface would be much easier than floating the same distance from the surface of the earth.  For that matter, it would also be possible to note what's visible and what's not at different distances from the inner surface.

A little back-of-the-envelope estimation suggests that one would have to be able to see objects kilometers or tens of kilometers away.  By way of comparison, Earth's oceans are quite dark at a depth of one kilometer, so this seems like a longshot.  Nor does it help that it's possible to hear long distances, since sound doesn't necessarily propagate in a straight line (neither does light, but that's a different can of worms).


As I originally disclaimed, it's not a good idea to rule something out as impossible just because you can't think of a way to do it.  The inhabitants of a subsurface ocean would have thousands, if not millions, of years to figure things out, even if they wouldn't have the advantage of already knowing approximately what their world looks like.