The article is a little bit breathless about this work as though evidence of solar system instability is completely novel and unexpected, but investigation in the area using simulation isn't exactly unprecedented.
Gerry Sussman and Jack Wisdom were working on the question of solar system instability in the late 1980s and Sussman and his students built a specialized computer called the Digital Orrery at MIT. They ran some very long simulations and found strong numerical evidence that the orbit of Pluto is chaotic.
The point the article (apparently unsuccessfuly) tries to hammer home is that the findings here are mathematical, they go beyond simulation and take a deeper bite into the problem, proving that all planetary systems are unstable.
The first paragraph of the linked article talks about simulation experiments from 2009, so your criticism here that there is some spurious claim to novelty is pretty unfounded. Simulation runs that show instability are old hat; mathematical proof that this instability is inherent and unavoidable is the story.
The article implies this is what was proved, but later contradicts itself. Based on my reading, only a couple specific initial conditions were proved to be unstable.
Yep. Quantum chaos, at least insofar as I was involved with it, is about semi classical analysis of quantum systems which would have chaos if they were classical.
Remember quantum mechanics started with the Bohr atom which was an approach that would generalize to any system that has quasi periodic (solar system in the short term) dynamics. Circa 1917 Einstein wrote a paper that said that this approach wouldn’t generalize because Poincaré proved that chaos is generic, soon after that we got Schrodinger’s equation and similar approaches. (Although that Einstein paper killed a line of development it barely got cited for 50 years)
Later on there were mathematical developments in quantum chaos such as Gutzwiller’s trace formula and also numerical work where people discovered various properties of the quantum levels of systems that were classically chaotic.
Linear operators in quantum mechanics don’t precluded observing chaos in the real world because the true “long term” is very long indeed. That is, classically or quantum mechanically if you wait some really absurdly long time (say much more than 10^120 years) the universe is expected to come arbitrarily close to the state it is in today. See
Though note that the recurrence theorem applies to a finite phase space. An expanding universe such as ours is not subject to that. We just get heat death instead.
These are numerical simulations though. The novelty is the proof that these instabilities don't come from numerical artifacts, but are an inherent part of the system.
There’s no doubt at all that there is some chaos in the solar system (e.g. you can’t quite predict which side of the sun the Earth will be on in 100 million years) but the question is does something big happen, like a planet getting ejected. In a low number of configuration space dimensions (N=2) you get “KAM tori” in phase which are an absolute barrier to the evolution of the system so chaotic motion is hemmed in. In N>2, however, KAM tori are still there but it is possible for chaotic trajectories to go around them. It’s clear that the trajectories of the planets behave like KAM tori on short timescales (1000s of years, that is how each one seems to be on an independent stable orbit) but what happens in the long term is not clear at all.
Early in the article, we get a discussion of the precession of Mercury, known for centuries. Then:
> (In this context, Newtonian mechanics gives such a good approximation of reality that these models don’t need to consider the effects of general relativity.)
But wasn't the precession of Mercury already known to be inadequately explained by Newtonian gravity, even before Einstein?
The precession of mercury has a few contributions. The largest is the tug of planets (500 arc seconds/century), the next largest is from general relativity (50 arc seconds /century). There are other, smaller contributions stemming from the sun being oblate. Knowledge about the anomaly in the precession was partly what motivated Einstein, and was one of the early predictions of the theory.
Am I deserve those downvotes? I consider that my answer is too cocky but the question is definitely about the scientific consensus and I did my best to imagine what the consensus could be like at that time, considering the so hard to believe conception about non-linearism in speed. For me, the conception of relativism was the hardest to believe among all science fields I stepped in.
I think the proof shows that these kinds of systems can be stable without any rebalancing for very long periods of time but then suddenly they are not.
no way. Earth orbital speed is 20,000 m/s. Meteroites are about the same speed. Earth mass is 10^25, total meteorite mass / day is 44t, or about 4x10^4.
Generously assuming all meteorites hit from the same direction, given the mass of the meteorite swarm is 1e-21 smaller, the total delta v is 10 to the minus 16. Double integrate that, and you get x^2/20000000000000000
Set equal to your desired difference, say one meter. You get over 100,000,000 days. That's 273,973 years to affect a 1 meter difference in position in the worst case.
Slingshotting voyager shifted the position of Jupiter by 0.0000000000000000000000000005 meters, or about 2 trillionths of the diameter of a proton. The mass of spaceprobes are nothing compared to planets.
Interesting because there are 100,000,000,000 stars in the galaxy. If even a small percentage have unstable systems there are going to be quite a few stray planets floating around.
We just don't find a stray planet without a sun because the entire way we find exoplanets is through their suns. Doesn't mean they don't exist. There are probably many more strays than non strays.
Perhaps we should consider why exactly are we living in something likely described as the most beautiful star system in our galaxy. The overall beauty of layout, the variety and the perfectly spaced orbits is something we may no longer take for granted. The fact that Moon has the same apparent size as the Sun, too.
It is also a cold, calm beauty for technically developed species instead of immediate joy of having multiple visible hot Jupiters in the system.
A few things about this idea.
1. It is much easier to detect large extra-solar planets than small, earth-like ones, which probably accounts for the preponderance of them in extra-solar surveys. I think its naive to conclude the solar system is so unusual.
2. The Trappist system isn't all that different from our own. Even detecting one similar system in our neighborhood suggests that they may be more common than the exo-solar planetary surveys so far have revealed.
3. You seem to be implying the existence of some supernatural force which has arranged our solar system. Or perhaps just a very powerful force. But, given the scale of the universe (or even just the galaxy) and the utter lack of direct evidence for either supernatural forces or ultra-advanced aliens, it seems like, on balance, the explanation "we just got lucky, planetary resonances, etc" combined with "the major edifices of human knowledge are consistent with this explanation" seem sufficient to make the hypothesis of "big dudes built the solar system" seem absurd.
Couldn’t what we find beautiful be emergent from where we find ourselves to begin with? It seems extremely arbitrary to try to define what’s beautiful about any star system.
The puddle looked at itself and its surroundings. The puddle saw that it had a very peculiar and specific shape, and yet its surroundings matched it perfectly. "It's amazing that the world is shaped just right and fits me perfectly" thinks the puddle.
I would argue that any kind of aliens will see our Solar system as beautiful because everything is regularly spaced, a great variety of all kinds of planets and moons, planetary rings, etc.
We take all that for granted, but it really isn't. Many of other solar systems we know contain an irregular set of planets.
The spacing of the planets isn't due to random chance. They are all in orbits defined by resonances with the other planets, as they effect gravitational drag on each other. They have pushed and pulled on each other for billions of years, until they have settled into the ordered structure we see today. https://en.wikipedia.org/wiki/Orbital_resonance
It could also be well possible that this sort of stability is required for multi-billion year evolutionary processes to take place. Systems with more chaos would likely also have chaotic seasons even if their planets were to have the other needed conditions for live. If the summer-winter cycle were more unpredictable that it is on earth, maybe that acts as a limit on the complexity that live can achieve as it would constantly be getting pruned back.
Systems with "unstable" or "irregular" planetary arrangements are probably just in an earlier stage of development, and might likely lose planets or push them into more stable orbits eventually.
Similarly "stable" or "ordered" systems are likely just older systems which have been able to develop without being disrupted by outside phenomena. In that sense looking for well structured systems might be a good place to start looking for life, as they are likely old and stable enough to have had evolution take place.
I suppose what I’m wondering is if those features would matter at all to other species. They’re highly salient to us from micro to universal scales, but other species might not even have a sort of mental construct for that notion to begin with. Perhaps it’s possible to be advanced and still have that kind of detail be present and visible yet not interesting or beautiful.
This might be another piece of the puzzle of Fermi paradox. Life is not much younger than universe. Maybe we owe development of life to the unusually lucky period of stability in our solar system right when the life began to be feasible here.
I think there's a very good chance that we are one of the first intelligent species in our galaxy.
Only for the brief period of time they happen to be in line with it. For orbiting planets, we can see these occlusions happening multiple times and thus filter them out from the noise, but there are countless reasons the light from a star could briefly dim once. We can find bodies within the solar system as they'll occlude multiple stars in a row as they move along, but for rogue planets to move far enough across the sky to occlude another star would take millennia.
They didn't seem to account Sun's global warming. In 500 million years it will boil out all the Earth oceans, and in 1 billion years it will swallow Mercury, Venus, Earth.
TA found instabilities that can occur on a scale of a few hundreds of millions of years. But yes, nothing to worry about on the timescale human civilization is likely to last
Notice that this is about new, particularly wild, solutions of the multi-body problem. By Kolmogorov-Arnold-Moser theorem, such unstable solutions form a negligible set among all possible initial conditions. The solar system is, still, stable with probability one.
Perhaps you can explain why you think KAM somehow proves this while there are simulations - and this new work - which prove the opposite.
Those models are all perfectly Newtonian. The solar system isn't.
It's usefully Newtonian on the timescales we use to push things around it. But over much longer timescales planetary orbits are influenced by variations in the solar wind, visits from external objects, redistributions of mass in the Kuiper Belt and Oort cloud, and so on.
These are mostly tiny influences, but enough to make claims of unconditional stability rather questionable.
[Disclaimer: not an expert on ODE, so I don't really know what I'm talking about]
I was just astonished by the title of the article, because it seemed to contradict KAM. Yet, upon careful reading, you can interpret the title in that "a solar system model" is unstable, but not all of them. Which does not contradict KAM.
If I understand it well, KAM is compatible with the following two sentences: (1) the set of stable initial conditions is of volume 1 in phase space (2) the set of unstable initial conditions is dense in phase space. Like the rationals are dense inside the reals, but still most reals are irrational.
What is the case here? I'm not knowledgeable enough to read past the abstract of these publications.
Gerry Sussman and Jack Wisdom were working on the question of solar system instability in the late 1980s and Sussman and his students built a specialized computer called the Digital Orrery at MIT. They ran some very long simulations and found strong numerical evidence that the orbit of Pluto is chaotic.
https://en.wikipedia.org/wiki/Stability_of_the_Solar_System#...
These weren't obscure results; further work was published in Science. See "Chaotic Evolution of the Solar System," in
https://www.science.org/doi/10.1126/science.257.5066.56