Hunt for trojans

Hello commanders and fellow explorers,

may I have your attention for a moment please? I'm not talking about some virus on your ship's computer or ancient history. I mean systems containing stellar bodies on Lagrange points in them.
I admit, the topic is a little clickbait :)

What are Lagrange points and these trojans?
I think Wikipedia describes Lagrange points very well:
In celestial mechanics, the Lagrangian points [...] are positions in an orbital configuration of two large bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two large bodies; the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
https://en.wikipedia.org/wiki/Lagrangian_point

So what does that mean? It means that it is possible for a smaller planet to be on L4 or L5 of a larger planet and share the same orbit. Both planets are on a stable orbit. In astronomy objects on these points are also called trojan. More details can be found on this page: https://en.wikipedia.org/wiki/Trojan_(astronomy)

How to find and validate
First, you need an advanced discovery scanner to find all bodies in the system. Then you need to check if two or more fulfill the following requirements (scanning them with a detailed surface scanner might help too):

Trojan (L4/L5): Because the two bodies form an equilateral triangle with the star it is relatively easy to validate if it's a trojan or not. Look on the system map and check the arrival point distance. The distance should be the same and both planets can't be in a binary system with each other. Upon scanning both of them, their orbital stats (orbital period/inclination/eccentricity and semi major axis) should match. To validate, fly next to one of the two planets and check the distance to the other one. If the distance between the two and to the star is the same, they form an equilateral triangle and thus it's a trojan.
However, it could be possible one of the two bodies is a binary system itself. That makes it harder to find and validate because the arrival distances might be a little off. If you turn on orbit lines, the orbit of the single body should go right through the binary system. Because binary systems don't show orbit lines around the star it should be pretty obvious which orbit line it is.
The most difficult and probably the rarest case if it even exists, are binary gas giants/dwarf stars with a trojan of binary planets. There is nothing else except their arrival distance to measure unfortunately.

This image shows what I mean:

The distance to the arrival point of the gas giant and the water world and the orbital stats are the same. But they are not in the same binary constellation.

L3: According to the Wikipedia page this orbit should not be stable. But if you happen to find one, their orbital stats should be the same, they should be on the opposite side of the star and the distance between the two should be twice the arrival distance.

L1/L2: No idea how to find them. Tell me if you know.

How to submit
I think the best way is to create at least 3 screenshots:
  • Stats of scanned first planet
  • Stats of scanned second planet
  • Distance between the two while being next to one of them
Then upload them to an imgur album, somewhere else or just as your reply to this thread. You don't need to have an imgur account to upload screenshots or to create an album. Just go to the imgur front page and drag and drop them in there :)
Here's an example of what i mean: http://imgur.com/a/MUEoE

It would be nice if you run a tool like EDMC, EDDI or EDDiscovery which transmits the scan data to sites like EDSM and EDDB but it's not a requirement.

List of systems and possible candidates
I created a google spreadsheet that contains all known systems with a trojan in them. It also contains some possible candidates which I extracted from the EDDB data dumps but need verification.

A few google sheets tips
I added a few filters you can easily use:


You can also sort:


And if you need something more like adding your own distance: make a copy of it (file -> make a copy)

Thanks for your time and help and to FDev for creating this galaxy with so much detail.
 
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I've been on a lookout for things like this since day one. Just, in case....
I'm yet to see one in almost 70,000 visited systems. :(
 
So far only one of these has been reported to the Galactic Mapping Project, but I really have no idea how rare these are in the game...

I have never noticed one myself, but since these are not obvious from a casual clance of the system map, many may have gone unnoticed...
 
I've been on a lookout for things like this since day one. Just, in case....
I'm yet to see one in almost 70,000 visited systems. :(
Good luck :)

I went through the entire EDDB database which are about 12 million systems and 7-8 million bodies currently and there are only 58 systems currently in that list that have a high chance of having one. The orbits of 2 bodies are the same when it's declared as "maybe" so all it needs is some validation. As for finding new ones: keep you eyes open. Who knows how many systems contain trojans but have not been discovered yet or not fully scanned.

So far only one of these has been reported to the Galactic Mapping Project, but I really have no idea how rare these are in the game...

I have never noticed one myself, but since these are not obvious from a casual clance of the system map, many may have gone unnoticed...
That's why I compiled the list with the help of the EDDB data dump. I wanted to see if there are more and if I can find them.
 
In the prequel games (FE2 and FFE), Trojan moons and planets were deliberately excluded from the procedural generator, but the Eta Cassiopeia system was deliberately hand-crafted to have two ELWs in Trojan orbits, one on either side of the gas giant aptly named "Between". I seem to recall going there in my very early days of ED and being disappointed to see the planets were all still there but their orbits had been redesigned to remove the Trojanity.
 
I have found one of these before, but I don't have the system name immediately to hand. I think I mentioned it on a forum post somewhere, I will try to dig it out tomorrow.

(eta)

I didn't find mine yet, and now I remember more clearly it was a situation where two planets were sharing the same orbit in approximately the positions where trojans would sit, rather than a large planet preceded or trailed by others. Still it was cool.
I managed to find this mention by Andrew Reid of a similar case.
 
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You know, I've been under the assumption that these wouldn't have been modeled in the game at all. Maybe that's a terrible assumption, when you consider how much they DID model, such as common barycenters and binary/trinary objects, and so on. I could have passed through dozens of these and I wouldn't have noticed, partially because I keep the orbit lines turned off, for a more immersive view (playing in VR).
 
I'm currently checking out a few systems that could contain shepherd moons but the gas giants are missing a ring!?

https://eddb.io/body/2638681 should have 3 rings with a large gap in between but I can only see the A and B ring in the game. And when I calculate the the orbit of Moon A using Keplar's formula I come up with a semi major axis of roughly 240,000 km which should place it between ring B and C...

Edit: I calculated the density per km² of all the rings and ring C is much much lower compared to A and B. Maybe it's not in the game because of that.

You could check out HIP 9203, HIP 15937 and Alnitak to look for shepherd planets (if that's also a thing). No guarantee that there are any. I got it out of the EDDB dumps :)
 
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Found one! way out in the Near 3kpc Arm.

I just happened to notice something odd about the distances, then I searched the forums and found this thread. Awesome!

Eos Audst FS-W c1-24 2 is a gas giant, with a smaller thick atmo planet (3) in the L4 or L5 Lagrange point. Not sure if it's leading or trailing, I didn't take the time to figure out how I might check that part.

It's also interesting to note that there is a 60° difference between the two arguments of periapsis. I'm not sure, but I think this is probably required for the orbits to be stable. It's definitely required for mean anomaly (which we can't see), as that's part of the definition of the Lagrange point. Alas, we are missing some orbital elements in game (and journal) for no good reason that I can think of, since the game must use them to place planets and orbits correctly.

Imgur album or spoiler tag below
 
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Never noticed this thread before - great work, Camulorix. This gives me something extra to look for while I am out exploring.

Also, well done, cmdr underhill for the find!
 
I didn't get any email about your posts. I will check and update the spreadsheet soon.

Edit: I added the 2 systems to the spreadsheet
 
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I'm delighted to report I have just found a trojan system of my own: it lies in the Nuekuae IZ-D d13-1356 system, in the Colonia Road region just 728 LYs from Gandharvi, 2270 LYs from Polo Harbour and 1489 LYs from Gagarin Gate. The trojanity is certain, although the complexity of the orbits with the involvement of a third co-orbiting planet means it is not entirely obvious. I was running EDD when I stumbled upon the system, so EDSM knows all the details of the planets involved.

Here is the system map; I have crudely photoshopped it to add the position pointer info for all three relevant planets, showing distances from the arrival point. The "Anchor" for the trojan system is Planet 1, a Class IV gas giant of 3167 earth-masses. Planet 2 is co-orbiting Planet 1, and makes Planet 1's position wobble a little, but not by much, since at only 3 earth-masses, Planet 2 is much less massive than planet 1.


Planet 3 is therefore technically in the L4/5 trojan point of the Planet 1/2 system's barycentre, rather than of Planet 1 itself. As evidence, I submit these three photos. First, I flew up above the plane of the solar system and as you can see, the positions of the star (lower left), the Planet 1/2 system (top) and Planet 3 (lower right, selected) form a perfect equilateral triangle. You can also see that, with the orbit lines on and Planet 3 selected, Planet 1/2 lies exactly on the orbital path of the orbit of Planet 3.


Finally, I flew down to Planet 3 and hovered at this position over the planet's pole. Then called up the navigational panel. Behold, the central star and Planet 1 are at the same distance from Planet 3, 1181 Ls.

 
Trojan or collision candidate?

I may have found a Trojan pair - but the reason I say 'may' is that their orbit lines do not perfectly coincide, although both orbit lines pass through the body of both worlds.
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Ploi Aec PN-B d13-42 5 and 6 are not co-orbital on the system view but have the same orbital distance from the star, as far as I can determine given that 'planet' 5 is a Y dwarf and the distance is not given: I use the distance to its innermost moon, which is in a very close orbit:

From a distance they appear to share the same orbit:
From the vicinity of each world, the other is the same distance away as the star, to within 1ls.

However, when up close, it is apparent that their orbital lines are very slightly different, although each does pass through the body of both worlds:

So are these truly Trojans, or does the slight difference in orbits suggest that there will be a collision or interaction at some point in the future? Or perhaps gravitational interaction with the Y dwarf planet 7 keeps them apart somehow?
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It was a total fluke I came upon this system at all, never mind noticing that planets 5 and 6 had the same distance from the star as I was scooping, yet were not shown as a binary pair in the system view. I had just taken a slight diversion from my route to visit the Hawking's Gap Alpha base, which is only a few hundred LY away, and had departed there on course for my next destination when I encountered this system.
 
If you really wanna dig deep into it, you can check what the semi-major axis and orbital periods are in the journal. Much better resolution (metres and seconds). If the periods are different, they will eventually collide (maybe some thousands of years in the future).

I don't know what amount of difference in the other orbital elements is possible in reality before the orbital period would no longer stay in lockstep with the partner's orbit.
 
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