Alright. Finally got it working and it's very rough but should get somebody started.
Note: Updated to allow for multiple orbits to check for intersection of orbits
Lunar Orbit and Parallel Orbit for Ruins
Here's, for example, the first site. Indeed the ruins fall right on the line.
To use this download and extract the pages here and open it directly on your desktop
https://www.dropbox.com/s/4k4asdu9lboal9n/lunar-ruin-orbitalpath.zip?dl=0
Gather 2 latitude and longitude readings for a given moon using the following method
In supercruise get the moon as close to the top of the targeting UI as possible and then drop your altitude down below the DRP indicator as seen here.
This allows you to use your escape vector as a direct overhead pointer to line up with the moon.
Line it up as perfectly as possible and then note the in game date/time and latitude and longitude of your ship.
Do this twice and enter these coordinates as the Lat/Lon and the radius in km and hit calculate. What you'll get is a visual display of the orbit and the parallel one the ruins should be found on.
A text output with the lunar orbit and the parallel one is also ourput so you can fly from one to another.
Some caveats:
1. Ideally I'd like to host this somewhere. Just don't have anywhere to do so. If you do and would like to please message me.
2. I'm using a map so the orbit can be visualized. Even though the earth is used in the background the proper radius is being used for distance calculations.
3. You have to refresh the page to run a new calculation. I need to add a clear to remove existing markers, etc.
Here's what it does.
1. Use coordinate 1 and coordinate 2 to get a bearing.
2. Use this bearing and coordinate to generate a great circle arc
3. Taking the original bearing if it's greater than 180 then the orbit is moving in such a way that the ruin will be southward. Otherwise northward.
4. Get 44% of the radius. This will be the distance to use in km from each given point.
5. Continually add km in distance to this great circle from step 2 and get the new coordinate. That's a point on the sphere. Repeat this process for the for every x km in the diameter. This actually just gives us half the points.
6. For each new point get its bearing. rotate plus or minus 90 degree and then get a new coordinate from that bearing that is the offset distance we calculated in step 4. This new point is the point in our parallel orbit.
Repeats the above the antipodal which gives us the other half and also ensures our coordinates are ordered in such a way that they are seamless.
Credits:
and mostly the calculations and methods from
http://www.movable-type.co.uk/scripts/latlong-vectors.html
I want to thank Suteksio for helping gather coordinates and others for helping to bounce around the math needed to make this work. The library had the tools for it... just had to wrap my head around what had to be done.
As well as Bram Armitage for helping calculate distance ingame so I could verify my tangent and radius calculations
For any questions please message me AdmlAdama on the frontier forums
https://forums.frontier.co.uk/member.php/149570-AdmlAdama