Horseshoe Orbits

Question

I'm envisioning a series of moons in orbit of a super-earth (ideal) or gas giant. If technically workable, the super-earth would have earthlike gravity, the mass and size aren't important. If it's too hard to make it terrestrial, I can use a gas giant. What is important are the moons: 7 earthlike. In addition, there are another 5, smaller, habitable moons/planetoids which themselves orbit the 7 primaries and have roughly earthlike levels of gravity, if not the same density and mass.

Speaking of mass, I'd love to keep all of these moons as small as possible, while keeping earth gravity, but haven't worked out the math on that. I know that this could work in standard orbitals (though the number may be high), but I'd love to have the 7 operate in a horseshoe orbit, and I'm wondering how many objects can share an orbital by using horseshoe orbits.

This is probably a bit complex, so just to recap:

The Star: 'H' A central planet: 'N' 7 earthsized Primary moons & 5 orbiting Secondary moons: D&p V&r, W&i, E, A&z, L&s, F

Can those moons, share a single, complex, horseshoe orbit?

I'm thinking based on the sizes, that the primaries could simply be binary pairs with their secondaries. None of the primaries have more than one secondary, anyway, and it could help make the physics work.

The original idea was simply to have them on different orbitals to the giant, or to have them in a stable ring, spaced out on the same orbital, alongside an asteroid belt, but the horseshoe concept may work better with other things that I won't get into here, and I'd love to know if that high a number is possible.

There are 'magical' elements here, but I'd like to keep them out of the system structure as much as possible. Part of this concept is one original super-earth, which was fragmented into the moon system. I'm thinking maybe a civilization dragged a gas giant inner-system to create a brown dwarf, for a dyson sphere or something, and ended up failing spectacularly, and breaking a large terrestrial planet into fragments later captured by 'N'.

I simply can't find any solar system modelling tools that are complex enough to handle this or tell me if there are stable solutions given the constraints. (P.S. if you know of a tool that can do that, I'd love to know).

Answer 1

Can those moons, share a single, complex, horseshoe orbit?

Perhaps not as many as you describe, but the situation is plausible. Saturn's moons Janus and Epimetheus share a horseshoe orbit.

However, you will need to invoke some of the magic you describe. Earthlike moons means a massive planet, one that cannot be Earthlike because you require the high gravity to keep Earthlike moons in orbit. So, without the magic, you would be forced to give up the habitability of the planet.

Answer 2

Short answer: the gravitational relationships between this planet and moons will not be realistic. You'll have to make it work with either technology or magic.

You might want to check out Pierson's Puppeteers from Laryy Niven's Known Space series. They've mechanically arranged five planets around a star; it's not quite the same as what you're describing, but you'll run into similar problems.

https://en.wikipedia.org/wiki/Pierson%27s_Puppeteers

https://en.wikipedia.org/wiki/Klemperer_rosette

As the second link points out, these configurations are inherently unstable:

...any motion away from the perfect geometric configuration causes an oscillation, eventually leading to the disruption of the system (Klemperer's original article also states this fact). This is the case whether the center of the Rosette is in free space, or itself in orbit around a star. The short-form reason is that any perturbation destroys the symmetry, which increases the perturbation, which further damages the symmetry, and so on. The longer explanation is that any tangential perturbation brings a body closer to one neighbor and further from another; the gravitational imbalance becomes greater towards the closer neighbor and less for the farther neighbor, pulling the perturbed object further towards its closer neighbor, amplifying the perturbation rather than damping it. An inward radial perturbation causes the perturbed body to get closer to all other objects, increasing the force on the object and increasing its orbital velocity—which leads indirectly to a tangential perturbation and the argument above. [Emphasis mine.]

And that points in the direction of why your proposed system will also be unstable. The fact that they are sharing a horseshoe orbit actually makes the configuration you want less likely. You basically have seven planets with similar densities in a Klemperer rosette, and an eighth planet providing the tangential perturbation to their orbits.

Answer 3

Short version Magic can do anything but this whole thing will purely scream "a Wizard did it!"

You can't keep this from obviously flouting the laws of physics. Without intervention "basic" three-body horseshoe orbits are not stable over geological time as it is and what you are describing, if I read this right, is in fact a system with at least 14 celestial bodies; a stellar primary orbited by a Gas Giant (a super earth would not, I believe, provide sufficient Barycentral mass to stabilise such a complex system) which is in turn orbited by 7 earthlike worlds that in turn have 5 sub-satellites on the same order of size as the earthlike satellites of the Gas Giant, this system is inherently unstable and, without intervention, would shed satellites or sub-satellites into stellar orbit, or maybe into the deep void depending on the exact energies involved, ever time there's a resonance event.

Without obvious and massive magical intervention you can forget about horseshoe orbits, most of the proposed orbital system will fly apart in a matter of years. Most of the magic is not where you might think it is either, you'll need magic to keep the worlds in this strange artificial system in their orbits but you'll need a an awful lot more magic to keep the worlds themselves intact. Every resonance event that is magically prevented from moving the involved bodies out of orbit is going to instead transfer massive amounts of energy into those bodies. In the natural course of things this would end up being expressed as heat, one way and another, a lot of heat, (estimates for previously discussed artificial orbital structures suggest per orbit energy inputs on the order of the full mass conversion of small stars are needed to manipulate earth-mass bodies) if that's not magicked away in turn then every ball of rock in the system will be molten in a couple of days and vaporised shortly thereafter.