Navigating in a Subsurface Ocean

Question

Based on the planet from this question. The main thing that distinguishes this planet from, say, Europa, is the handwavium light-source, which I must assume is wrapped in a perpetual explosion wrapped in strong currents, due to the extreme temperature difference. How extreme this would be varies as things stabilize, so let's say we're talking after things have settled down as much as they will.

Intelligent creatures on this planet would probably be able to estimate their distance from the light-source, even if they can't see it (would they even evolve vision, since the light only goes so far through the water. The currents will have predictable directions for quite a distance, so relative positions aren't too hard.

But is there a way to determine something analogous to lattitude and longitude? The planet has at least one satellite. I'm not sure if it would have a magnetic field separate from the handwavium (if it does, that seems like it could solve the problem).

Since they have the light-source as a reference point, just one of lattitude or longitude should be sufficient. Ex, if they can tell that they are so far north or south of the LS, the rest is simple geometry.

Alternatively, if there is an established theta = 0, they can just use polar coordinates, with the LS as the origin. But is there a natural way to establish theta = 0, and identify where one is relative to it?

If it makes a difference, I imagine the LS being north of the equator, though how far is not firmly established.

Answer 1

Assuming that they can see or sense the source of illumination when it is not obstructed by the core of the planet and that source is location under the ice surface.

In these conditions they can calculate their distance (r) from the light source perhaps by using relative luminosity with a dimmer light source indicating a more distant light source according to an inverse square law.

But in order to obtain an absolute location using polar coordinates they need to determine the angle from the light source and to do this they would need to rely on some directional information.

This could be by way of a magnetic field or it could be by way of landmarks but if there is no magnetic field and the ice and core are featureless then this will not be possible.

However if they have sophisticated instrumentation they might be able to detect any number of sources of asymmetry that might be used as a basis for navigation such as variations in the gravitational field of the orbiting satellite.

Answer 2

Multiple light sources.

This sidesteps the problem of one colossally bright source. Also the different sources would be named, like stars. You could tell how close you were to any given light source because of its color - in water the spectra drop out with distance starting with red and blue being the last to go. A distant light source would be deep blue. Closer would be green and very close would be all colors.

With one light source and a known distance from it, there is a sphere around the source and you could be anywhere on the sphere. With 2 sources and known distance from each you can be anywhere on a circle. But with three sources there is only one point at known distance from each.

Persons navigating your world could choose among various visible light sources and take sightings to ascertain position. I like the idea of glasses with lenses of different colors to take a distance sighting on a given light source. You would flip thru them and gauge accurately the distance according to which color blocked view. For example if I can see Jones' point thru the yellow lens (but not the red) but I can only see Slarty's point thru green and further, I know Jones is closer than Slarty.