The Scanning and Location Problem

A couple weeks ago, I posted a math problem that I was playing around with. This problem was born of our some ideas for my new role-playing game, as well as the basic scanning mechanism of EVE Online.

In EVE Online, if you are trying to scan down an object in space, you launch some probes and they report back the distance from the probe to the anomaly, with some amount of error, up to some maximum range. Your ship’s computer then aggregates that information and renders it as an overlay on the scanning screen. If two of your probes received responses, you would get a circle where the two spheres intersect, with three you would get two points, and with four you would get a single point (with some degree of error). You then decrease the range of the probes (increasing their signal strength) to narrow in on your target – a pretty simple and fun min-game which tickles my imagination and makes me think I know something about how science fiction scanning might occur.

For my role-playing game, I wanted to turn that on its head – suppose an object in space wanted to be found, what would be a low-tech way to say, “I am here, precisely.” My idea was to send a probe to each of three planets with two pieces of information: how long the probe took to get from its launch point to the planet, and the locations that the other two probes were launched to. As I was thinking this through, I realized that if the object wanted to be found, and only sent out three probes, than they must be sufficient to locate the object (i.e. it is the only point that would satisfy the constraints). The question I had then was, if the three probes are sufficient, are they also necessary, which lead me to the proof that only two probes were necessary to locate the object so long as three were sufficient and the object was within the triangle formed by the three points.

This lead me to an interesting thought: how could we broadcast our location, precisely, to another world with the least amount of encoding? What would a sort of intergalactic “We are here” message look like? I was inspired by the article on the signal that LIGO picked up over at The Physics Mill and wondered if such rare events would help. Suppose we retransmitted the signal of the black holes along with the some other unique signal (such as a supernova) to a star system coplanar to both galactic events and Earth, could that signal be interpreted correctly to be simple coordinates to our planet?

In any event, this is the genesis of these mathematical ideas that stick in my head and make me think…

Category(s): Pseudorandom
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One Response to The Scanning and Location Problem

  1. If the probes encoded their location in the polarization of the signal, or if the detector were sensitive to orientation, you could do better than in-plane with only two probes. You could (potentially) localize to a circle. In the context of gravitational waves, I wrote about that here:
    http://www.thephysicsmill.com/2016/03/06/direction-ligos-gravitational-waves/