So I've been working on a project where I modify the Solar System, and I originally had a small gas planet(like 5-10 earth massses) named Juno orbiting between Jupiter and Saturn. However, as it turns out, the area between Jupiter and Saturn is rather precarious - when I ran the system in a simulation the two gas giants ejected my precious little Juno from the Solar System within 1 million years or so. I don't want all the worldbuilding work I put into Juno to go to waste, however, so I'm thinking that Juno could be a Lagrangian companion to Jupiter, sharing the giant planet's orbit. The idea isn't too ludicrous - a lot of asteroids(the Trojans) do this exact same thing. However, this is not an asteroid - this is a rather massive planet. When I ran it in the simulation it surprisingly seemed to be stable, but I want to ensure that it remains stable over billions of years. So could my gas dwarf share Jupiter's orbit?
Nip Dip says they ran a simulation of the set up and it seemed to be stable - for the time period covered.
But they ask about stability over a period of billions of years, indicating their simulation didn't cover that long a period.
Astrophysicist Sean Raymond does similar simulations of solar system evolution as part of his job. And he says:
I am available to help out with ideas for books, movies, games or any other projects set on other planets. My specialties are:
World building: creating scientifically accurate settings for storytelling
Understanding what it would feel like to live on other (custom-built) worlds. How would the stars move? What would the weather be like?
Testing the scientific validity of already-created settings.
And you should consider:
As a rule of thumb, the system is likely to be long-lived if m1 > 100m2 > 10,000m3 (in which m1, m2, and m3 are the masses of the star, planet, and trojan).
So according to that rule of thumb, a Jupiter trojan would have long time stable orbit if the trojan had a mass less than 0.0001 that of Jupiter or less than 0.03178 that of Earth.
I note that some of the imaginary planetary systems Raymond has designed on his blog seem to feature trojans which break that rule of thumb. Raymond has also done simulations with planets in stable rings or arcs. If anyone knows of exceptions to that rule of thumb and is able to calculate them Raymond would seem to be a good choice to start asking.
And if it is impossible for Juno to have a long term enough stable orbit as a Jupiter Trojan, Raymond be able to find a more stable place in the solar system for you to put Juno.
You should also consider the scale of science fiction hardness.
If you are content to have a low score in that scale, like star Wars, for example, you can put your fictional planet Juno wherever you want without worrying about how plausible the orbit is.
stable over billions of years
Over a handful billion years you will have planetary migration. According to some current models, gas and ice giants will move a lot. There is even an hypothesis suggesting that Jupiter and Saturn moved inward, then outward since they formed.
While L4 and L5 Lagrange points are considered stable, such migration and the the interactions with a protoplanetary disc make your arrangement very improbable.
I think a more plausible way to have such an arrangement is if your planet is a recent capture, having come from another system.