Lagrange systems: What is the mass range for a gas giant if I want to place a earth-like planet on L4 and L5
I am wanting to make a 3 world lagrange system around a Sol analog star that includes 1 gas giant and 2 terrestrial worlds with large moons. I want the terrestrial worlds to have a similar gravity to Earth (about 80-120% of Earth's gravity) and also be able to support liquid water and carbon-based life, the moons can range from the mass of Ceres to that of Mars for now.
My question is how large does the gas giant have to be to support 2 of these systems at L4 and L5?
Right now I am being safe and going for super-jupiters, but since I also want a gas giant that can support a habitable moon I am afraid something with the mass and magnetic field of Jupiter might just be far to hostile to life for my liking, so I really want to find the minimum mass of a gas giant that can support this type of system.
To address some of the concerns listed:
First off, the shape of the orbit of the gas giant. It has to be close enough to the star to support liquid water and can't stray out of that zone around the star. For simplicity's sake, it is roughly circular, it would have a super low eccentricity with the periapsis and apoapsis being relatively close together
Secondly, do not worry about whether this system could form over millions of millions of years. Pretty simply, this system is created by the author and there doesn't need to be a natural explanation for how it could've formed. It was born that way, you could say. Similarly, the period of stability doesn't need to be long, though I would like it to naturally be stable across a timescale of many million years simply because I don't want a distant large object, like another star less than 1/2 a lightyear away from destroying it. If it matters, the simple context is that it is part of a four/five-star system. I say four/five because it's really a four-star system, but a small red dwarf star is on a collision course with a distant sub-system of the four-star system and it will make contact in roughly 16 000 years. For the structure of the system, if this matters. We have a one-star Sol analog sub-system far away from an s-type sub-system with 2 sub-systems inside it, one of the sub-systems is a p-type two-star and the other has one star.
Basically: Y-*. If that doesn't make sense, the "Y" is the large subsystem and the "*" is the small sub-system, the "-" is a symbol showing that these two subsystems are connected. The subsystem we are discussing is the "*" subsystem, the P-type system is represented by the "V" part of the "Y" and the small super-subsystem is the "l" part of the "Y". We are discussing the small subsystem which is the "*" in the diagram.
If the fifth star is included, we have (not to scale) this diagram: >Y-* which basically tells you that the oncoming star is on the opposite side of the system as the small sub-system which we are talking about. Whether this structure works is admittedly it's own question but I won't get into that.
When it comes to the stability of this system, I want it to be stable enough that gravitational forces from around 6600 AU away won't ruin the darn thing in short order. The system should hopefully last about 24 000 years in these conditions because that is how long the history runs. Simply put, there doesn't need to be a system stable enough for life to develop, because life is placed there artificially.
Currently, I don't have time to address the rest of the concerns, but I will see if there is anything else I need to address later.
This post was sourced from https://worldbuilding.stackexchange.com/q/163825. It is licensed under CC BY-SA 4.0.
1 answer
Both this site and Wikipedia assert that L4 and L5 are stable for a mass up to about 25 times the mass of the secondary. Since plain old Jupiter is about 318 Earth-masses. Since a) 318 is more than 10x larger than 25, and b) L4/L5 are nowhere near any moons orbiting the secondary, I would have to guess that, if these points are stable at all (and I think they would be if you want to "cheat" and have no other planets in the system), then it is plausible that two Earth-mass planets could sit at L4 and L5 of a planet with "merely" Jovian mass... or even smaller; no need for a "Super-Jupiter".
As We Are Monica notes, I don't have a supercomputer¹ to prove this, but your audience won't either. Ergo, my "official" answer is that this appears to pass a "reasonable suspension of disbelief" test.
(¹ TBH, I'm not sure how a supercomputer would help.)
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