Interesting! Both the phenomenon itself, and the fact that there are two totally different explanations in the answers (“yes”, and “no - it’s a coincidence”), and it therefore seems the true answer is “we aren’t sure”.
In astronomy we call these resonances. Sometimes, two seemingly unrelated periodic events will occur together, synchronized by a ratio between some small integers.
I think the most typical example is the one they teach you in the first Solar System 101 class to wow you (it works): the 3:2 resonance between the orbits of Pluto and Neptune.
Sometimes it might turn out to be a coincidence with more accurate measurements, or when you find evidence that this moment in time might be somehow unusual.
For example, Earth and Venus also seem to be in 8:13 orbital resonance, but, in fact probably aren't. On closer inspection, it turns out that there is error of about 0.4% after 8 years and it compounds. It takes a while to compound, but effectively you can't use this "near resonance" to predict where the two will be in their orbits in a few thousand years.
In fact, with enough bodies in the solar system and the birthday paradox, there are many compelling candidate resonances with small integer ratios, but the majority of them are probably just random coincidences.
Just to clarify the difference between "true" resonance and a coincidence:
True resonance reinforces itself. For example, Pluto speeds up and slows down in its orbit as it passes Neptune and the exchange of energy between the two works out such that the lowest energy state is a 2:3 resonance, so that's where they would end up even if you "poked" the system a little.
A coincidence is not self-reinforcing. If you "poked" the system, it would disrupt the ratio and it'd stay disrupted.
Sometimes, the preconditions for resonance might disappear, and then you end up with a coincidence at a nearly perfect ratio that slowly drifts afterwards. The opposite also happens.
Of the 5 Lagrange points, 2 are stable. If you poke an object at one of the 2 stable points, the object begins to orbit in a circle around that invisible point.
But it is also possible, perhaps likely, that some coincidences are in fact higher-level resonances between groups of planets. These would be multi-body problems that may take thousand or millions of years to react to perturbations. The calculations for these may well be beyond our current capabilities to detect (3+ body problems).
Second of all, it’s not random. In music, near resonances are more consonant than perfect resonances. And, orbital resonances tend to disrupt stability (eg, if earth and Venus were in an orbital resonance, then they would often pull at mercury really hard, potentially pulling it out of orbit).
Previously, I opted not to give my rationale for the hypothesis in case someone had any reason to refute it.
How would anyone even refute a vague statement like that?
Secondly, the word "consonant" has many different definitions, so again, your statement could mean almost anything. The concept of consonance has no obvious connection to whether or not a system is stable.
"Orbital resonances tend to disrupt stability" - that's not true, especially not the thing about Mercury. The influence of the pair on each other would be great, and either cause the resonance to fall apart or, more rarely, to lock in. But mercury's orbital period is not in a simple ratio with the resonant pair, so nothing would be meaningfully different.
Look, I can tell from your profile that you're a professor in some kind of social science. Is it possible that you're, like many people in academia, under the influence of a cognitive bias that makes you think your expertise in one field should somehow transfer into insights in a completely different field?
And, again, showing up and just saying "hypothesis: whatever" is something people can either ignore or engage with, but if you really wanted to engage, you would try to say something concrete instead of just making yourself look clever.
In music, consonance is stable, dissonance is unstable.
“ Notes that sound good together when played at the same time are called consonant. Chords built only of consonances sound pleasant and "stable"; you can listen to one for a long time without feeling that the music needs to change to a different chord. Notes that are dissonant can sound harsh or unpleasant when played at the same time”
- https://www.earmaster.com/music-theory-online/ch05/chapter-5....
Orbital resonances tend to be unstable:
“Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists” — https://en.wikipedia.org/wiki/Orbital_resonance
But you said orbital resonance between two planets will eject a third from its orbit. Just... no. A physicist would never make a claim like "an orbital resonance between Earth and Venus would disrupt Mercury" without a study to back it up.
As an aside, it is the the fact that you say things like this with confidence really sets me off - people who do know what they're talking about are careful to point out speculation. Our intuitions don't map so well to borderline non-newtonian complex interactions. Only a fool would claim otherwise.
You can't just show up to another field and use your observations and a wikipedia page to make good points. I'd be happy to recommend astrophysics literature if you want.
Your uses of words "stable", "unstable" and "consonant" and "dissonant" are the key here - I have no idea what "stable" means in music theory, and I don't think you'd know what I mean when I say "metals", because every field has its own jargon. But I'm not trying to make a point about music, whereas you are trying to make a point about astrophysics. Fine - but you can't expect to be understood or paid attention to if you don't learn the jargon and the underlying physics.
> Previously, I opted not to give my rationale for the hypothesis in case someone had any reason to refute it.
Maybe I misunderstand but it sounds like you are saying that you thought the reasoning for your hypothesis would not be accepted, you didn't want others to critique its potential problems, but you wanted people to read it anyway.
Well, it would help explain why these near resonances could be more valuable to the solar system’s stability than perfect resonances. Meaning they likely aren’t coincidental, despite not being perfect.
Meta: a few years ago, HN was interested in on-topic discussion by informed people. Nowadays, the "informed" bit is irrelevant. It was inevitable that this place would become reddit, and now it has. Calling out incorrect information or pseudo-intellectual responses and nonsense has become unpopular. Fine, I'll stop doing it.
Please do avoid thinking you can identify “pseudo intellectual responses and nonsense.” Check out my paper reviewing the concept of resonance across fields — the most largest such review of resonance ever.
That is a very interesting paper, and I like that people do cross-disciplinary comparative studies, but you can't expect a study like that to give you insights into orbital mechanics.
Yes, there are surprising correspondences in physics, mathematics and music. But they've never held predictive value - they're the kind of thing that seems beautiful and obvious once you know about it, but to my knowledge, no music theorist has ever made a useful prediction about sympathetic resonance in ship building.
The Karate Kid couldn't really learn karate by painting a fence.
I apologize for ranting about pseudo-intellectualism, that was harsh. I do hope you can see why this type of empty quip can provoke people. People actually study this stuff for years with rigor. If someone shows up without obvious credentials, makes a provocative non-point that seems to ignore the fundamentals of your field, and expects you to treat their points as valid, then you might think that person is displaying hubris. For me that was too much before my second coffee.
First off: I think your response was totally reasonable given the lack of any useful or understandable point made in that comment. The hypothesis as given was begging to be asked, "on what basis?" It was almost as if they wanted to be called out so they could share their paper.
Regarding Karate Kid: I don't remember the movie, but I think you are bring too reductionist about reductionism. You can't learn karate by painting a fence, but leaning karate can teach you something about your body mechanics that can help you better paint a fence. And while geology is not astrophysics, learning about groundwater flow and dam construction might provide insights or new considerations into orbital mechanics with regard to how to handle the interaction of masses in a frame of gravity. I am friends with an astrophysicist and acoustics engineer and they seem to gain a lot from each other in their discussions of waves and analysis of measurements.
Regarding music and ship-building: Less known is that Leonardo da Vinci, famous for his paintings and engineering, painted "The Last Supper" with the mathematical help of his friend (possibly lover) Luca Pacioli. The Franciscan monk whose widely disseminated "Summa de arithmetica" gave us double-entry bookkeeping, even he really mostly repackaged the work of the artist Piero della Francesca, who in turn was riffing on Archimedes.
Of course the fields aren't predictive of each other, not exactly. But it can offer new questions or insights. An Archimedean "Eureka" often precedes the proving (or disproving) of the rule. And while that is a mere moment and it takes years of work to follow, regardless of whether you prove something out with words, figures, or art, I think it's that moment that gives the impetus to everything that follows. Sadly, I never trained as an artist, and I have trouble "reading" paintings as communications of geometry. The Tower of Babel seems to extend beyond mere words.
It's easy to see why people might overfit on the Eureka moment, but it might not ultimately be an overfit for humanity at large: it takes a collective to build a body of knowledge.
Another good example is when you're listening to music in the car and think your turn signal is perfectly in time with the song, only to have it slowly drift off once you notice.
I can see how orbital mechanics would lead to these sorts of small-integer ratios being true for arbitrary periods and then disappearing, yet this fact still seems unintuitive/unsatisfying somehow.
I think it's because we're so all familiar with quantum electrodynamics now, that it actually seems somewhat counterintuitive that the (stable) orbits of planets aren't quantized valence shells!
Prepare to openly and unabashedly hate on me and hit your downvote button:
Some post here at some point did some analysis that concluded that Mercury was "the closest" or something for every planet for some analysis or other because Mercury is closest to the Sun.
Both Mercury and Venus are closer to the Sun than Earth is and if you study astrology this means Mercury is never more than one sign away from your Sun sign and Venus is never more than two signs away and both very regularly appear to "run backwards" (called retrograde in astrology).
Which is where you got those bizarre and complicated geocentric models of the solar system from before someone said "Oh, wait, if you assume the Sun is at the center of this, not the Earth, then it vastly simplifies everything and makes sense a la Occam's Razor/find the simplest explanation."
Astrology and astronomy used to both be studied as one subject under the heading astrologia and astrology means "the study of the stars" and astronomy just means "the naming of the stars" presumably because when the two split it was sort of a pointless hobby for people rich enough to own a telescope and if you found a new one, you got to name it.
Anyway, the point being, Venus and the Earth are -- shockingly -- both locked in orbit around the Sun, thus the phrase "solar system," and as a wild assed guess from some ignoramous who mostly is interested in astrology, not astronomy, that there is your so-called "tidal locking" mechanism.
It's a known fact that the point all bodies in the solar system orbit around is not actually the centre of the sun, but some point close to the sun, known as the barycentre of the solar system[0]. This moves around based on the exact configuration of the planets (where they are in their orbits).[1] By definition, this barycentre can only be considered 'locally'. For example, there is another 'barycentre' for the whole milky way, and presumably for the whole universe.
Mercury is the 'closest' to all planets on average over time due to the fact it is closest to the sun (or more accurately, this barycentre), and due to an unintuitive but completely logical consequence of Mercury having a small orbit[2].
The last paragraph of your comment I was not able to properly understand. It is certainly true that the 'solar system' is made up of objects which rotate around the sun. But that's the definition of 'solar system'. Just as the 'milky way' is made up of objects which rotate together... including the solar system. It's just useful for us to have a term for our local corner of the universe.
My point is people have trouble mentally modeling the solar system and seem to do a poor job of distinguishing a geocentric model from a sun-centered model and sometimes sloppily mix the two which goes weird places.
I like that there was no way even to guess that this coincidence occurred until we became able to scan Venus with radar. Visually, all faces of Venus are indistinguishable.
I wonder whether we have the moon to thank for Earth having retained a short day, and the short day for our magnetic field. Big moons of inner terrestrial planets must be vanishingly rare in the galaxy. If terrestrial planets with magnetic fields are uniquely suited to breed up complex life, that might by itself account for the Fermi paradox.
But I don't know how to evaluate the notion that our gross moon has protected Earth from the near tidal locking Mercury and Venus suffer.
What is it that would make big moons of terrestrial inner planets vanishingly rare?
And how likely is it that a planet without a large moon would fail to retain a short day? Mars has a day of similar length to that of Earth (though no magnetic field worth speaking of...).
If it is a coincidence then perhaps this case of "correlation is not causation" is explained by both planets having some magnetic interaction with the sun and perhaps the interaction with the sun determines rotational behavior of planets (speculation). I read sometime ago about "magnetic flux ropes" https://www.frontiersin.org/articles/10.3389/fspas.2020.6059...
Also I read time ago there is a "cometary" aspect to venus and it's "tail" touches the earth, which might also be in the same realm of physics (electromagnetic interactions leading to rotational behavior)
Basically the inner planets seem to follow a pattern in their spacing from the Sun - and some of the outer-planets which were actually discovered after the law...
...but it's not a great correlation, and you need to have some hacks (e.g. including Ceres as a planet) to make it work...
So, mainstream Astronomy has relegated it to the edges of the field, and into the realm of amateurs and crackpots.
It's interesting though that apparently a similar pattern in the distances between planets seems to occur in those systems with multiple extrasolar planets that we have observed. But it still may be a mathematical artefact.
One way to explain this curiously geometric composition of the solar system is to note the analogy with drum modes or even electron shells: suppose the sun's gravity produces a very slow oscillation that creates a stable pattern of nodes and antinodes, and planets naturally slide into those spots over billions of years.
To be fair, Ceres was considered a planet at one point and it is now the closest dwarf planet to Earth. So, in that sense it is a planet but it is not a major planet.
40 comments
[ 2.5 ms ] story [ 90.9 ms ] threadIn astronomy we call these resonances. Sometimes, two seemingly unrelated periodic events will occur together, synchronized by a ratio between some small integers.
I think the most typical example is the one they teach you in the first Solar System 101 class to wow you (it works): the 3:2 resonance between the orbits of Pluto and Neptune.
Sometimes it might turn out to be a coincidence with more accurate measurements, or when you find evidence that this moment in time might be somehow unusual.
For example, Earth and Venus also seem to be in 8:13 orbital resonance, but, in fact probably aren't. On closer inspection, it turns out that there is error of about 0.4% after 8 years and it compounds. It takes a while to compound, but effectively you can't use this "near resonance" to predict where the two will be in their orbits in a few thousand years.
In fact, with enough bodies in the solar system and the birthday paradox, there are many compelling candidate resonances with small integer ratios, but the majority of them are probably just random coincidences.
True resonance reinforces itself. For example, Pluto speeds up and slows down in its orbit as it passes Neptune and the exchange of energy between the two works out such that the lowest energy state is a 2:3 resonance, so that's where they would end up even if you "poked" the system a little.
A coincidence is not self-reinforcing. If you "poked" the system, it would disrupt the ratio and it'd stay disrupted.
Sometimes, the preconditions for resonance might disappear, and then you end up with a coincidence at a nearly perfect ratio that slowly drifts afterwards. The opposite also happens.
What would happen if you poked at object at one of the Lagrange points? e.g. the James Webb Space Telescope.
Second of all, it’s not random. In music, near resonances are more consonant than perfect resonances. And, orbital resonances tend to disrupt stability (eg, if earth and Venus were in an orbital resonance, then they would often pull at mercury really hard, potentially pulling it out of orbit).
Previously, I opted not to give my rationale for the hypothesis in case someone had any reason to refute it.
Secondly, the word "consonant" has many different definitions, so again, your statement could mean almost anything. The concept of consonance has no obvious connection to whether or not a system is stable.
"Orbital resonances tend to disrupt stability" - that's not true, especially not the thing about Mercury. The influence of the pair on each other would be great, and either cause the resonance to fall apart or, more rarely, to lock in. But mercury's orbital period is not in a simple ratio with the resonant pair, so nothing would be meaningfully different.
Look, I can tell from your profile that you're a professor in some kind of social science. Is it possible that you're, like many people in academia, under the influence of a cognitive bias that makes you think your expertise in one field should somehow transfer into insights in a completely different field?
And, again, showing up and just saying "hypothesis: whatever" is something people can either ignore or engage with, but if you really wanted to engage, you would try to say something concrete instead of just making yourself look clever.
Orbital resonances tend to be unstable: “Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists” — https://en.wikipedia.org/wiki/Orbital_resonance
Try curiosity over judgement.
As an aside, it is the the fact that you say things like this with confidence really sets me off - people who do know what they're talking about are careful to point out speculation. Our intuitions don't map so well to borderline non-newtonian complex interactions. Only a fool would claim otherwise.
You can't just show up to another field and use your observations and a wikipedia page to make good points. I'd be happy to recommend astrophysics literature if you want.
Your uses of words "stable", "unstable" and "consonant" and "dissonant" are the key here - I have no idea what "stable" means in music theory, and I don't think you'd know what I mean when I say "metals", because every field has its own jargon. But I'm not trying to make a point about music, whereas you are trying to make a point about astrophysics. Fine - but you can't expect to be understood or paid attention to if you don't learn the jargon and the underlying physics.
Maybe I misunderstand but it sounds like you are saying that you thought the reasoning for your hypothesis would not be accepted, you didn't want others to critique its potential problems, but you wanted people to read it anyway.
What value does it add to the discussion then?
https://www.frontiersin.org/articles/10.3389/fnbot.2022.8504...
Yes, there are surprising correspondences in physics, mathematics and music. But they've never held predictive value - they're the kind of thing that seems beautiful and obvious once you know about it, but to my knowledge, no music theorist has ever made a useful prediction about sympathetic resonance in ship building.
The Karate Kid couldn't really learn karate by painting a fence.
I apologize for ranting about pseudo-intellectualism, that was harsh. I do hope you can see why this type of empty quip can provoke people. People actually study this stuff for years with rigor. If someone shows up without obvious credentials, makes a provocative non-point that seems to ignore the fundamentals of your field, and expects you to treat their points as valid, then you might think that person is displaying hubris. For me that was too much before my second coffee.
Regarding Karate Kid: I don't remember the movie, but I think you are bring too reductionist about reductionism. You can't learn karate by painting a fence, but leaning karate can teach you something about your body mechanics that can help you better paint a fence. And while geology is not astrophysics, learning about groundwater flow and dam construction might provide insights or new considerations into orbital mechanics with regard to how to handle the interaction of masses in a frame of gravity. I am friends with an astrophysicist and acoustics engineer and they seem to gain a lot from each other in their discussions of waves and analysis of measurements.
Regarding music and ship-building: Less known is that Leonardo da Vinci, famous for his paintings and engineering, painted "The Last Supper" with the mathematical help of his friend (possibly lover) Luca Pacioli. The Franciscan monk whose widely disseminated "Summa de arithmetica" gave us double-entry bookkeeping, even he really mostly repackaged the work of the artist Piero della Francesca, who in turn was riffing on Archimedes.
Of course the fields aren't predictive of each other, not exactly. But it can offer new questions or insights. An Archimedean "Eureka" often precedes the proving (or disproving) of the rule. And while that is a mere moment and it takes years of work to follow, regardless of whether you prove something out with words, figures, or art, I think it's that moment that gives the impetus to everything that follows. Sadly, I never trained as an artist, and I have trouble "reading" paintings as communications of geometry. The Tower of Babel seems to extend beyond mere words.
It's easy to see why people might overfit on the Eureka moment, but it might not ultimately be an overfit for humanity at large: it takes a collective to build a body of knowledge.
> Please don't post shallow dismissals, especially of other people's work.
From https://news.ycombinator.com/newsguidelines.html
I think it's because we're so all familiar with quantum electrodynamics now, that it actually seems somewhat counterintuitive that the (stable) orbits of planets aren't quantized valence shells!
Some post here at some point did some analysis that concluded that Mercury was "the closest" or something for every planet for some analysis or other because Mercury is closest to the Sun.
Both Mercury and Venus are closer to the Sun than Earth is and if you study astrology this means Mercury is never more than one sign away from your Sun sign and Venus is never more than two signs away and both very regularly appear to "run backwards" (called retrograde in astrology).
Which is where you got those bizarre and complicated geocentric models of the solar system from before someone said "Oh, wait, if you assume the Sun is at the center of this, not the Earth, then it vastly simplifies everything and makes sense a la Occam's Razor/find the simplest explanation."
Astrology and astronomy used to both be studied as one subject under the heading astrologia and astrology means "the study of the stars" and astronomy just means "the naming of the stars" presumably because when the two split it was sort of a pointless hobby for people rich enough to own a telescope and if you found a new one, you got to name it.
Anyway, the point being, Venus and the Earth are -- shockingly -- both locked in orbit around the Sun, thus the phrase "solar system," and as a wild assed guess from some ignoramous who mostly is interested in astrology, not astronomy, that there is your so-called "tidal locking" mechanism.
Mercury is the 'closest' to all planets on average over time due to the fact it is closest to the sun (or more accurately, this barycentre), and due to an unintuitive but completely logical consequence of Mercury having a small orbit[2].
The last paragraph of your comment I was not able to properly understand. It is certainly true that the 'solar system' is made up of objects which rotate around the sun. But that's the definition of 'solar system'. Just as the 'milky way' is made up of objects which rotate together... including the solar system. It's just useful for us to have a term for our local corner of the universe.
[0]: https://www.skymarvels.com/gallery/Vid%20-%20Solar%20System%... [1]: Satellites (both natural and artificial) also orbit this point when you map their path over the course of a full orbit of the body they primarily orbit: e.g. the moon orbits the Earth, but over the course of a year, the moon and Earth together orbit the barycentre of the solar system. [2]: This GIF shows it quite logically: https://engaging-data.com/pages/scripts/orbits/mercury-faste...
My point is people have trouble mentally modeling the solar system and seem to do a poor job of distinguishing a geocentric model from a sun-centered model and sometimes sloppily mix the two which goes weird places.
I wonder whether we have the moon to thank for Earth having retained a short day, and the short day for our magnetic field. Big moons of inner terrestrial planets must be vanishingly rare in the galaxy. If terrestrial planets with magnetic fields are uniquely suited to breed up complex life, that might by itself account for the Fermi paradox.
But I don't know how to evaluate the notion that our gross moon has protected Earth from the near tidal locking Mercury and Venus suffer.
And how likely is it that a planet without a large moon would fail to retain a short day? Mars has a day of similar length to that of Earth (though no magnetic field worth speaking of...).
Also I read time ago there is a "cometary" aspect to venus and it's "tail" touches the earth, which might also be in the same realm of physics (electromagnetic interactions leading to rotational behavior)
Basically the inner planets seem to follow a pattern in their spacing from the Sun - and some of the outer-planets which were actually discovered after the law...
...but it's not a great correlation, and you need to have some hacks (e.g. including Ceres as a planet) to make it work...
So, mainstream Astronomy has relegated it to the edges of the field, and into the realm of amateurs and crackpots.
It's interesting though that apparently a similar pattern in the distances between planets seems to occur in those systems with multiple extrasolar planets that we have observed. But it still may be a mathematical artefact.