Is this some kind of mathematical thing based on how orbits work, or is it more like natural selection, in that any moons that don't avoid each other just aren't there anymore.
It is a mathematical thing based on how orbits work. Orbits that are very close to a resonance but not quite there will tend towards being even closer, so it's a stable system. If this wasn't the case, you wouldn't ever expect to observe anything like this, due to disturbances to the orbits (from other bodies tugging gravitationally on the objects) building up.
So could two earth-sized planets be in resonant orbits around a sun that would otherwise intersect? If so, what does this mean for the definition of a planet as something which "clears the neighborhood"?
It would be if we saw many colliding orbits and only those that had resonance surviving in long run.
But resonances are perfect ratios and no random orbits will ever have perfect ratios of orbit times.
Instead what happens is that collisions seem to be extremely rare occurrence. Once two moons find themselves on close orbits they will tend to exchange energy until they find some kind of resonance that will keep true for a very long time until disturbed.
Resonant orbits might not be natural selection, but they might participate in a form of thermodynamic selection: two simple forms and structures selecting for and reinforcing one another.
They are both subsets of the same thermodynamic processes of structures/arrangements sticking arouns when they mutually support one another creating persistence in a chaotic system
My understanding is that some folks believe there are similar mechanisms underlying the emergence of both -- a generalized form of selection between mutually reinforcing structures that encode elements of prediction of the chaotic environment they reside in, be that the periodicity of orbits (that "know* a stable path that will reasonably persist) or life itself (that have similar baked in prediction abilities we perceive subjectively as consciousness).
Disclaimer: biochemist, technologist and armchair follower of complexity science
The idea is that the gravity of a moon affect the trajectory of the other moon and vice versa, until they are in resonance. It's a bad analogy, but it's closer to Lamarckism than Darwinism, but it's still a bad analogy. There are nothing similar to random mutations.
By natural selection I meant that if you have two (or more) bodies on the same orbit they'll crash or they'll find stable orbit (resonance). Of course you see resonating ones because ones that wouldn't would collide millions of years ago.
I agree that in principal most things are natural selection. The things that are not on a current time (a certain proportion of which bound to exist) frame are behaviors that will eventually be eliminated.
Resonance plays an incredibly large role in orbital mechanics [1]. All of the orbits of the moons of Jovian planets are in small fraction ratios of one another.
I often wonder if some of the simplifications we commonly teach do more harm than good. "Small thing orbits big thing" is one of them, "a thrown ball follows a parabola" is another one (it's true on a flat earth, but in reality you launch the ball into a highly elliptical orbit that just happens to intersect earth's surface after a few meters).
These simplifications are often conceptually not that much simpler, they just have much simpler math. But saying "x is what's happening, but in these circumstances we can treat it as y" is an important skill in science and life, we should teach it more (and benefit from fewer misunderstandings caused by teaching only the simplification)
Topological a torus, yes, but the area exposed to atmosphere was approximated as a sphere. Lol, we all giggled at the approximation. He drew a trunk on the sphere later!
Not quite -- orbital mechanics are Hamiltonian, which means they conserve energy, phase space volume, and often a bunch of other things. Dynamical systems that conserve phase space volume cannot have "strange" attractors (attractors with zero volume) like the ones described in the article.
Those are horseshoe orbits in a rotating reference frame (your link does not provide the caption). Janus and Epimetheus do orbit around Saturn elliptically (except when they switch positions) when seen from an inertial frame.
The orbits probably wouldn't look very fancy if you were observing from Saturn (besides the speeding up and slowing down), but when seen from either of the moons, that's roughly what things would seem like to you.
> The orbits probably wouldn't look very fancy if you were observing from Saturn (besides the speeding up and slowing down)
Unless you were moving around the thing at precisely the right velocity I suppose. But it being a gas giant I suppose the point is kind of moot. It's not like you or a manmade device can stand touch down anywhere while still observing the sky.
"moving around the thing at precisely the right velocity" would be the rotating frame of reference that gives you the horseshoe orbits seen in chmod775's 2 links.
My point is that for people like myself, referential frames are not intuitive, and temporarily misleading. If they are unlabeled, one might even confuse them for the inertial frame, and then if one were uncritical enough, assume erroneously that these moons "bounce" back and forth like billiard balls (https://www.teachersource.com/product/newtons-kinetic-yoyo-s...).
It took a bit of searching, but here is an animation showing how the two moons look in the inertial frame of reference. The interesting bit is how they interact gravitationally so that the faster one never overtakes the slower one, rather it causes the faster one to slow down and the slower one to speed up and pull ahead.
There are now several dozen multiplanet exo-solar systems that exhibit various kinds of resonances. They are a real time laboratory for testing dynamics mathematics.
We're looking at billion-year-old hydrostatic, spheroid satellites that currently orbit in a system that stabilized a long, long time ago.
They are ancient survivors of a chaotic distillation that predates all of life on earth, a dynamic system that stands as a persistent, unchanging choreography, undisturbed in a quiet part of space for eons.
None of the bodies are engaging willpower, in order to avoid one another.
What scientists are observing just happens to be a closed circuit scale-model racetrack, and the little toy race cars couldn't jump out of their well-worn grooves if they tried.
It's amazing that we're still discovering stuff like this with large objects in our own solar system. It's humbling and makes me realize how much we still don't know.
Relative to Earth’s size, sure, but all the giant planets in the solar system have several large spherical moons, hundreds or thousands of km in diameter. These two rocks are small by any planet’s standards.
Wait. That would mean there are moons twice as big as Earth in our solar system. Jupiter has one that's bigger than Mercury, but still almost 10-times smaller than Earth.
