Hunt for trojans

Well, my algorithm seems to work for the subgroup of trojans at L4 / L5 of planets NOT in a binary system.

What do I do? (Go to ALGORITHM HERE to skip the boring details)

As usual, I work with the EDSM bodies.json-file which can be downloaded here.

I am NOT working with a database. It is on my list to learn that, though. That however may make it a bit easier for others to run the code I wrote (once I've cleaned, commented and published it) since it does not require knowledge of how to setup a database.

With >80 GB is the database far too large to work on it. So first I extract just the orbital parameters (and name and system name) for each body and save it after every 5000000 entries in a new file.
This takes quite a while on my 2012 laptop.

The problem now is, that the bodies that belong to one system can be scattered over several files because it is not sorted in the EDSM file.
Hence, I then compare the information of each file with each other file and take care of that every file contains complete system information. One could call this "defragmentation" of the data.
This takes also quite a while. Several hours in fact.

I'm pretty sure these two steps are NOT necessary if one works with a database.

So now I have a file which is separated into systems and each system contains the orbital parameters of each (reported) body of this system. Neat :)

< ALGORITHM HERE >

Then I check for each body in every system its name and compare it with the names of all other bodies.
In principle a trojan can't be a moon and must be on the same level.
So < FOO BAR AB 1 > can be a trojan to < FOO BAR AB 2 > but neither to < FOO BAR AB 1 a > nor to < FOO BAR CDE 2 >.

This is a remnant from when I tried to find trojans to binary systems.
For the reduced version of this algorithm I would just need to check if the "root" of the name is the same and the "counter" at the end one higher (or lower).

However, this gives me then all the trojan candidates in a system.

For these candidates I check then if orbital period, orbital eccentricity and orbital inclination are the same.
THIS will give me millions of binary system and a couple of thousand trojans.

Now I've made the curious observation that the difference of the argument of periapsis of the two planets in a binary system is exactly 180 degrees.
ATTENTION: THIS OBSERVATION MAY BE WRONG!

So, I simply exclude all of the candidates that have this difference in the value of their argument of periapsis.
Unfortunately will this also exclude all trojans at L3 (if they exist in the game).

Well, what I actually do is a bit different. I INCLUDE just candidates that have a difference in the value of their argument of periapsis of 60 degrees. But it was easier to explain the issue with the binaries the other way around.

Finally I look up the coordinates of the systems in which these trojans are but that is just of practical concern.

And that seems to work.

In the EDSM data from 3305-06-04 I found 4403 trojans (fromthe above mentioned subgroup) this way. Three of these I've confirmed.

If anybdoy wants to check some more, please tell me where you are and I will send you the three / five / twentythree / as many as you want closest to you.

@Orvidius: Do you want to make a list out of that? I could send you a CSV.
 
There may be a way to find trojans to binary systems. At least in the examples given here the distance to arrival of the larger of the two bodies in the binary system has always exactly the same value as the belonging trojan planet.

So first finding all binary systems and then checking if one of them has the same distance to arrival as a another planet on the same level in the same system may find those.

This however may still not find all trojans since the accuracy of the value of this characteristic is rather low. So for planets close to the main star this may not work since we than have digits behind the decimal separator.
This will also likely not work if the planets don't orbit the main star.
This will also likely not work in the case of two, approximately equally heavy planets in a binary systems. Assuming that the barycenter is then not identical with the heavier of the two and that the latter has a different value for the distance to arrival whereas the trojan will have an value equal to the one of the barycenter.
This may also produce many false positives due to planets around a star very far away. So I guess I will restrict the search to distances below 23 kly (or probably even below that).

mhmmm … I'll work on that later today … or tomorrow.
 
I'm pretty sure these two steps are NOT necessary if one works with a database.
Correct. :)

Now I've made the curious observation that the difference of the argument of periapsis of the two planets in a binary system is exactly 180 degrees.
ATTENTION: THIS OBSERVATION MAY BE WRONG!
...
Well, what I actually do is a bit different. I INCLUDE just candidates that have a difference in the value of their argument of periapsis of 60 degrees. But it was easier to explain the issue with the binaries the other way around.
That's a good observation. In binary pairs, their periapsis needs to be opposite each other. This is easier to visualize in terms of the apoapsis however, since their most distant points are also opposite. This is a good test for binaries, I think. For some reason I've been overlooking this. (slaps forehead)



@Orvidius: Do you want to make a list out of that? I could send you a CSV.
I can also throw together a script to look for them. This should be fairly straightforward, using these rules.
 
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I haven't had a chance to verify any of this, so it's not listed on the website yet, but I built a spreadsheet using similar rules. I added a column for distance from Sol, to make verification from the bubble area a little easier. The first copy didn't populate that column correctly, so it has zeroes. I'm regenerating it now, so by the time you see this, it may already be corrected.

File here: https://edastro.com/mapcharts/files/trojan-planets.csv

In this first test, it found 7951 planets. I'm mainly using the Argument of Periapsis to try to filter out the binaries by disallowing a difference of 180 +/- 0.2 (exclusive) degrees. It's also looking for the Orbital Period and Semi Major Axis to be within 0.1% of each other's numbers, and for the names to have adjacent numbers.

The script currently takes about 45 minutes to run. Definitely one of the longer ones.

EDIT: Using a database makes certain things a lot easier, but for a script like this, where it needs to compare millions of planets to find a small number of them with specific relationships, there are other problems that you have to work around. Huge database lookups can be very slow, and the script can end up using a massive amount of memory if you don't chunk the data in a sensible manner, and churn through it in batches.
 
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The other thing we should be thinking of is Trojan moons. I realise it's probably a lot harder to generate the mass difference required for Trojans with the Stellar Forge moon-making algorithms, but the only real-world Trojan objects we know of are moons in or own solar system.
 
Talking about moons. The above proposed algorithm to find trojans to binary systems is catching moons very effectively … … AAAARGHJAGRHJAG … I'm going nuts over this ;)

So … I have to limit the search further to mass ...ratios larger than 25:1.

Btw. shouldn't smaller leading co-orbiting planets be called greeks?
 
The other thing we should be thinking of is Trojan moons. I realise it's probably a lot harder to generate the mass difference required for Trojans with the Stellar Forge moon-making algorithms, but the only real-world Trojan objects we know of are moons in or own solar system.
Actually the first objects we knew of that were "trojan" were the asteroids at the L4/L5 points in Jupiter's orbit - others were subsequently discovered in the orbits of other planets, and then a few satellites were found (I think they're all in Saturn's satellite system?).
 
Hey all, I have a parital submission, having not known what I found until I was long gone. (Thanks, malenfant!) All I have is this:
Planets 1 and 2 of Cat's Paw Sector HR-W d1-29 are trojans. Their distance from the star and each other is 3548.78ls, and their both of their orbital periods are 6679.4 days.





 
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You don't need to go back. The Orrery and sector name is all you need :)

If you check the orbital parameters of these planets on EDSM you will see that you indeed found a trojan configuration :)
 
AAARGHGAHRGAHGHAGRHA (again) … the errors and mistakes in the EDSM drive me towards insanity bit by bit!
A distance to arrival of 0 ls … for ALL bodies in the system! Of course will that register as trojans.
 
Is anybody close to Hypiae Phyloi TI-A d1-11, Blau Aec GD-V c2-6, Juenae QW-F c700, Skaude AC-J d10-337, Grea Bliae CL-Y g2, or Dryae Eaescs AY-N b40-2? These are the only systems (registered by the above described algorithm) that have two trojan system on different orbits.
If this could be confirm that would be great :)
Some of those are trojans to stars. Do we count them as trojans?
One of them is a water world trojan :)

The algorithm above also seems to "catch" trinary systems. But just three of these turn up so I will consider the numbers / results still as valid.
I wonder though what made these trinary systems so special that they got "caught" by the algorithm but not the many other trinary systems that should exist.
 
I'm not near any of those, but Dryae Eaescs AY-N b40-2 is down near Explorer's End, which I was thinking of heading toward anyway. I'll try to remember, and I'll check to see if it's too far off my path.

Meanwhile I've been updating my spreadsheet script, and it's now including stars, and finding some triplets we might need to verify at some point. I added some loose constraints on eccentricity. It's probably looking pretty good, but I'm still thinking of this as a list of candidates until we know how reliable it actually is.

EDIT:
Triplet candidates:
Aunaiwyg AA-A h213 ABC 4,5,6
Choomeou QZ-W d2-334 2,3,4
Flyiedge FF-F b3-11 ABCD 2,3,4
/EDIT

My spreadsheet is here: https://edastro.com/mapcharts/files/trojan-planets.csv

I visited one at random near the bubble and it appeared to be legit (planets 3 and 4):

 
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Next, for the holy grail - are there any known Earth-likes in Trojan orbits? Even a terraformable might be cool, though I think searching for terraformability would be a bit tough.
 
Trojan ELW candidates:

(also, looks like 270 or so terraformables in the list)

Partner namePlanet NameType
Alpha Caeli A 5Alpha Caeli A 6Earth-like world
Bleia Eohn ZF-L d9-51 1Bleia Eohn ZF-L d9-51 2Earth-like world
Boelts SZ-X d1-336 4Boelts SZ-X d1-336 5Earth-like world
Boeph AA-H d10-325 ABC 1Boeph AA-H d10-325 ABC 2Earth-like world
Byoomiae UY-A d2780 1Byoomiae UY-A d2780 2Earth-like world
Eoch Flyuae ZF-N d7-479 1Eoch Flyuae ZF-N d7-479 2Earth-like world
Eoch Pri MG-X d1-36 A 2Eoch Pri MG-X d1-36 A 3Earth-like world
Eok Flyuae RJ-O d7-2577 1Eok Flyuae RJ-O d7-2577 2Earth-like world
Flyai Flyuae YM-Q d6-105 ABCD 6Flyai Flyuae YM-Q d6-105 ABCD 7Earth-like world
Flyooe Bli QF-C d14-124 1Flyooe Bli QF-C d14-124 2Earth-like world
Hypiae Aoc TS-U d2-2874 7Hypiae Aoc TS-U d2-2874 8Earth-like world
Pipe (stem) Sector ZE-A d101 2Pipe (stem) Sector ZE-A d101 3Earth-like world
Syralie SK-C d14-2 8Syralie SK-C d14-2 9Earth-like world
 
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