N Body Problem (?) - Solar System Complexities

[Ian J.]

Hi,

This is my first post here, so if I make mistakes please be gentle with me.

I have a 'problem' with a solar system I'm developing for a series of stories I'm writing. Those stories have nothing to do with Earth, and are set in a system unlike our own.

To introduce the system, the premise for it is that instead of being 'just' planets round a star, the habitable worlds are more like moons around a giant planet which orbits a star. The moons have orbits that are quite long, not dissimilar to Earth years in length, and the masses of the three principal moons is not dissimilar to that of Earth.

The specific issue I have is one of what I believe relates to stability of orbits. It is my preference to put two of the moons at 180 degrees to each other orbiting the planet with the third on a Lagrange point. So Moon 1 would be between L1 and L2 (much as Earth is today in our system related to the Sun), Moon 2 would be opposite and practically on L3, but Moon 3 would be on L4 or as near as.

Now as I understand it, this produces an out-of-balance system that won't work according to physics, but what I wondered is could a fourth body Moon 4 be introduced to the system in such a way as to counteract the imbalance and allow Moons 1 and 3 to stay apart from each other and also not slip into balance by being at 120 degrees from each other?

Any help with this would be much appreciated.

Note: it is my intention with my stories to try and keep away from erroneous physics where such physics are well known. I might have to stretch things a little bit when it comes to traveling around the galaxy/universe with regards to light speed, etc, but like many space opera writers I feel have little choice in that if I am to have an engaging stories that can appeal beyond the hard science fiction fans.

Cheers,

Ian J.

 

[SteamKing]

There are several gravity simulators available on the web to model a system like you hypothesize.

One such is Gravitation 3D: http://www.gravitation3d.com/

There is also Gravity 6: http://www.andersson-design.com/gravity/

 

[Ian J.]

Thanks for the links :)

 

[Ian J.]

Looking at the programs, it looks like Gravitation3D will likely be the best to use, or at least the most 'visually' useful. Now I just need to get to grips with how it works so I can work out what I'm trying to do.

Thanks again.

 

[lpetrich]

A word of warning. The sun's perturbations of their motions will almost be as large as the planet's pull on them. So watch out for instability.

That happens when the moons' orbit periods are almost as large as the planet's, and for the Lagrange points, they are exactly equal. In fact, L1, L2, and L3 orbits are always unstable, while L4 and L5 are stable only if the objects' masses are different enough.

If you want to do it empirically, you can find the orbit periods of the farthest moons with respect to their planets in the Solar System. I recall once doing so, and finding that the farthest moons are well within the planets' closest Lagrange points.

 

[lpetrich]

I worked it out. The farthest known moon of a planet relative to the planet's orbit period is Jupiter's moon S/2003 J 2. It orbits Jupiter with a period only 4 times less than Jupiter's around the Sun.

 

[Ian J.]

Many thanks for the replies. I've had to do quite a bit of rethinking of my solar system design, and co-orbital orbits are now discarded. Also, based on replies to the habitable zone thread I started, I've had to consider how large the orbits could realistically be, and come to the conclusion they are going to have be smaller than I originally intended. This now means I will have to undertake significant rewriting work as the moons' societies will be affected by the changes.