+1 Nice answer but not what I'm looking for. I've tried that and can't be bothered to sit around waiting for EDDB to work out the distances to Merope, or HIP 14909, or Col 70 Sector FY-N c21-3, and then guess which page of results the systems at the correct distance are on, then have to wait for EDDB to work out the distances for the systems on that page again, then find out it's the wrong page, then guess another page, etc., all whilst I should have been playing the game. And then what if a system isn't even on EDDB? It's not a foolproof method.
I need help.
Late to the party but here's my 2c. I believe most of the tools that were actually used to decode the unknown sites did it by downloading all systems within a set distance of Merope and testing those. That's certainly how my tool worked. There were a couple of systems that weren't in EDDB, but they were easy to find based on the nearest EDDB system. 99% of systems were already there as this is an extremely well explored area. This is the most practical method.
For a purely mathematical solution the technique you're looking for is trilateration:
https://en.wikipedia.org/wiki/Trilateration
You're on the right track, by the looks. This is how early mapping of the galaxy was done before the ED log included coordinates for visited systems. See this thread:
https://forums.frontier.co.uk/showt...-way-to-crowdsource-the-3D-system-coordinates
Here are a couple of things to know that may help with using this technique:
1. trilateration in 3D requires four points and distances to give an unambiguous answer. The UL only provides three distances to three systems so any calculation is going to give you two candidate solutions. (Think about how spheres intersect: in non-degenerative cases two spheres intersect to give a circle on a plane and a third sphere intersecting that circle will result in two points of intersection. A fourth sphere is required to determine which point is correct.)
2. the distances reported by the UL are not necessarily very precise. This is due both to the way the distances are encoded and also due to the way distances are calculated in ED (which has some error introduced due to rounding).
3. coordinates in ED are stored internally as fixed point numbers that have a precision of 1/32 Ly.
So the results will be imprecise, but if you're just going to eyeball the candidate solutions in the Galmap then they should be good enough. If you wanted better accuracy a good way to check would be to find the nearest 8 valid coordinates (i.e. the eight points that fall on the 1/32 Ly grid and that surround the candidate solution), and then calculate the distance from each reference to each of those valid coordinates, and then re-encode those distances and see which coordinates match the UL data. That's a lot of work to do manually though.
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