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This is some neat research (and related to some of the work I did in my PhD). For those who are just reading the comments, the authors are exploring the impact

This is some neat research (and related to some of the work I did in my PhD). For those who are just reading the comments, the authors are exploring the impact of general relativity on the stability of the Solar System. It's been known now for a few decades that the Solar System is only marginally stable [1]. The gravitational perturbations of all the planets on each other (though mostly coming from Jupiter) cause the orbits of the planets to change slowly over time. It turns out, though, that Mercury is the closest to unstable, and has a ~1% chance of being ejected from the Solar System in the next billion years. One of the interesting things about Mercury, is that general relativity has a non-negligible effect on its dynamics (the famous "perihelion precession" that Einstein explained). What the authors did in this paper is run a number of long term simulations of the Solar System with general relativity --- but then they switched it off at a random time. What they find is that after switching off general relativity the Solar System goes unstable shortly thereafter. So the stability of the Solar System is highly dependent on general relativity. As a side note, the second author on the paper is Hanno Rein, who wrote Rebound [2], which is a very cool state of the art gravitational simulator. If you ever want to play around with gravitational dynamics, that's what I'd recommend using. (And that's what they use in this paper.) [1]: This is not terribly surprising because it turns out that nearly every dynamical system with more than three bodies is only marginally stable on a timescale of order its own lifetime. [2]: https://github.com/hannorein/rebound https://github.com/hannorein/rebound

auntienomen 4y ago
Hanno Rein writes some of the prettiest C code I've seen. He also has a cool app, Exoplanets. Big fan!
cperciva 4y ago
This is not terribly surprising because it turns out that nearly every dynamical system with more than three bodies is only marginally stable on a timescale of order its own lifetime. Does this mean that it's highly likely that our solar system had more planets a few billion years ago?
- lisper 4y ago
  It's 100% certain, modulo your definition of "planet". Our solar system began as a cloud of dust, which over time accreted into larger and larger objects. During that accretion process, many objects large enough to be called planets accreted by colliding with each other. That's how earth's moon was formed, and it's very likely the cause of Uranus's extreme axial tilt and Venus's retrograde rotation.
  - cperciva 4y ago
    Ok, I'm thinking of the "cleared its orbital neighborhood" definition. So not the initial accretion process but after it reached a more modern-looking system of planets separated by mostly empty space.
    - lisper 4y ago
      Well, like I said, it all turns on how you define "planet". Comet Shoemaker-Levy impacted Jupiter in 1994, so before that there was one more body orbiting the sun than after. But I'm guessing that doesn't count because it was a "comet" and not a "planet". Meteors hit the earth and moon constantly, but again, not "planets". Orbiting bodies are eliminated regularly, either by impacts or by being ejected, the former happening much more often than the latter because the ejection window is smaller than the impact window. And the bigger the body, the less likely it is to happen because to be eliminated it has to hit or do a flyby of something bigger, and the bigger you get the fewer things there are that will do the job. Jupiter, for example, ain't goin' nowhere. At some point in the past we had a lot more Mercury-to-Mars-sized things floating around than we do now. How long ago the last one got eliminated is anyone's guess, but it was almost certainly a few billion years.
      - AnimalMuppet 4y ago
        > At some point in the past we had a lot more Mercury-to-Mars-sized things floating around than we do now. How long ago the last one got eliminated is anyone's guess, but it was almost certainly a few billion years. The last one hasn't been eliminated - we still have Mercury and Mars. You probably don't think of it that way because we think of the existing planets as constants, not variables.
fbdab103 4y ago
>What they find is that after switching off general relativity the Solar System goes unstable shortly thereafter. Not my field, and I only glanced at the figures, but I think "shortly thereafter" is something only a cosmologist could say without blushing. Unless I completely bungled the meaning (very plausible), the paper is using time on the scale of billions of years.
- lloeki 4y ago
  I guess the timescale was picked up to match the expected end of Sol's main sequence (in ~5 billion years) and its growth into a planet-engulfing red giant, in which case continuing with the model beyond the next order of magnitude becomes unrealistic. IIUC the instability time scatter plot shows that GR basically stabilises our local N body problem by one to two orders of magnitude in time scale (10^8~10^8.5 vs 10^9~10^10), IOW giving a 900~9000Myr extra vs being derailed by a Mercury-Venus collision in ~100Myr, which would indeed comparatively be "shortly thereafter" at these timescales. I did chuckle at the phrasing though. (Disclaimer: not my field either, so I may be 10^10 wrong)
- antognini 4y ago
  Hah, fair. As an astronomer I don't really blink when someone says that 100 million years is a short time period.
towei4uo34i3 4y ago
Neat. I was half-disappointed that they didn't use scmutils (like Sussman & Wisdom) : (
causi 4y ago
So the stability of the Solar System is highly dependent on general relativity. That seems a bit misleading. If you have a complex system that reaches a measure of stability over a large timescale and then change any of the underlying rules, it's going to become unstable. In this scenario there's nothing special about special relativity, it just happens to be the rules they messed with.
- infogulch 4y ago
  That's a fair criticism. If a dynamical system is stable under one model, it's not that surprising if suddenly swapping out the model causes an instability. Basically, different models have different stability islands, if you would. But the question remains, how dependent on GR is the long term stability of an N-body system in general? Here's an experimental idea: create a "random N-body system" generator, and compare what % of systems are stable under Newtonian vs Einsteinian physics models.
  - raattgift 4y ago
    > in general That's too broad to answer. Let's narrow to our solar system, or a close approximation, first. Below, I'll step up to more complicated arrangements, and binary black holes. These are only three or four families of (regions of) general curved spacetime; there is a very large infinity of other families one could reasonably associate with "in general". In a (model) solar system, there is a large central mass and several other objects with extreme mass ratios to the sun. There are interesting secular resonances among Mercury, Venus, and Jupiter, and between Earth and Mars, where that means that from time to time (over many orbits), the precessions of the near-to-the-sun parts of the planets' orbits match. These resonances may increase the eccentricity of the smaller mass's orbit, which can in extremis yeet the small body out of the solar system, or cause a collision between planets (e.g. Mercury's orbit may near aphelion cross Venus's orbit). For the Mercury-[Venus-]Jupiter the closeness of Mercury to the sun tends to break up the resonance enough to significantly stabilize the shape of Mercury's orbit. Any sort of slow-down on the inner body when it and heavier outer bodies are relatively close together with the sun is liable to suffice, and that's what the authors of the link at the top argue what we get with (good approximations of) GR. (The approximations used by the authors are a post-Newtonian expansion <https://en.wikipedia.org/wiki/Post-Newtonian_expansion https://en.wikipedia.org/wiki/Post-Newtonian_expansion> and numerical methods). Very roughly, thanks to the large central mass and the very different distances of the planets involved, the outer body rushes ahead or equivalently the inner body lags behind, which avoids stabilizing the resonance. Many -- possibly even most -- stars are in binaries, rather than singletons like our sun. Planetary orbits in a binary (or triple) star system are likely to be dramatically different. In binaries, the width and mass-ratio between the partners are relevant quantities. Triples can be arranged in all sorts of ways. PSR J0337+17 is one known arrangement <https://www.youtube.com/watch?v=oDgfqq_W_uM https://www.youtube.com/watch?v=oDgfqq_W_uM>. PSR B1620-26, a pulsar-white dwarf binary, has at least one planet. I have only weak intuitions about what Jupiter or Earth mass bodies would do in such systems, or even how to select a reasonably astrophysical set of initial orbital values. (There are known circumbinary planets. See <https://en.wikipedia.org/wiki/Circumbinary_planet https://en.wikipedia.org/wiki/Circumbinary_planet> and <https://sci-hub.ru/10.1007/978-90-481-8687-7 https://sci-hub.ru/10.1007/978-90-481-8687-7> in which Chapter 9 details how these can be simulated). It is not too fanciful however to suppose that periastrons could be close enough that post-Newtonian effects are non-negligible, even if the stellar masses are non-compact. That doesn't say much about whether secular resonances (in the sense above) are likely in such systems. I have no idea, but I'd guess they aren't forbidden. > compare what % of systems are stable under Newtonian vs Einsteinian [gravitation] That's what the authors do in their paper <https://arxiv.org/abs/2303.05567 https://arxiv.org/abs/2303.05567>, although "systems" here is a simplified model of the solar system (they discuss several simplifications and their justifications: the oblateness of the sun and the presence of moons are probably interesting "future work" but are most likely not going to result in large corrections see their §3.2). For non-isolated systems, interactions with the environment can magnify whether these properties drive dynamical stabilization (merger) or instability (fly apart). The authors in their other fresh paper even more freshly summarized at <https://astrobites.org/2023/03/14/chaos-planets-future-of-the-solar-system/ https://astrobites.org/2023/03/14/chaos-planets-future-of-th...> discuss how "environmental events" (nearby stars and their potential to approach our solar system) might lead to e.g. collisions between Earh and Mars, or an ejection of one or more planets into deep space. Astrobites has also freshly summarized another "environment can change orbits" (for 2-body + dusty environment) at <https://astrobites.org/2023/03/13/will-it-merge-investigating-how-gas-disks-can-determine-the-future-of-a-binary-black-hole-system/ https://astrobites.org/2023/03/13/will-it-merge-investigatin...>. ("Dust" in the GR sense of <https://en.wikipedia.org/wiki/Dust_solution https://en.wikipedia.org/wiki/Dust_solution>, rather than in the sense of fine particles of e.g. chalk that allegedly accumulate on sedentary GR theorists). > Here's an experimental idea Been done (and improving) for many decades. See for example Fig. 1 in <https://arxiv.org/abs/1105.1082v1 https://arxiv.org/abs/1105.1082v1>.
AdamH12113 4y ago
Since Mercury is the closest planet to the sun, wouldn’t it need the most delta-v to escape the solar system? What about it makes it the most likely planet to be ejected?
- jessaustin 4y ago
  It is less massive than the other planets. Momentum is conserved, so any escape scenario would see at least one other planet with a smaller orbit.
- bmitc 4y ago
  The solar system is a chaotic, dynamical, and n-body system though, so the 1 or 2-body problems involved in delta-v calculations are much more simple. In addition, Mercury's mass is low, relatively speaking.

auntienomen 4y ago

Hanno Rein writes some of the prettiest C code I've seen. He also has a cool app, Exoplanets. Big fan!

cperciva 4y ago

This is not terribly surprising because it turns out that nearly every dynamical system with more than three bodies is only marginally stable on a timescale of order its own lifetime. Does this mean that it's highly likely that our solar system had more planets a few billion years ago?

lisper 4y ago
It's 100% certain, modulo your definition of "planet". Our solar system began as a cloud of dust, which over time accreted into larger and larger objects. During that accretion process, many objects large enough to be called planets accreted by colliding with each other. That's how earth's moon was formed, and it's very likely the cause of Uranus's extreme axial tilt and Venus's retrograde rotation.
- cperciva 4y ago
  Ok, I'm thinking of the "cleared its orbital neighborhood" definition. So not the initial accretion process but after it reached a more modern-looking system of planets separated by mostly empty space.
  - lisper 4y ago
    Well, like I said, it all turns on how you define "planet". Comet Shoemaker-Levy impacted Jupiter in 1994, so before that there was one more body orbiting the sun than after. But I'm guessing that doesn't count because it was a "comet" and not a "planet". Meteors hit the earth and moon constantly, but again, not "planets". Orbiting bodies are eliminated regularly, either by impacts or by being ejected, the former happening much more often than the latter because the ejection window is smaller than the impact window. And the bigger the body, the less likely it is to happen because to be eliminated it has to hit or do a flyby of something bigger, and the bigger you get the fewer things there are that will do the job. Jupiter, for example, ain't goin' nowhere. At some point in the past we had a lot more Mercury-to-Mars-sized things floating around than we do now. How long ago the last one got eliminated is anyone's guess, but it was almost certainly a few billion years.
    - AnimalMuppet 4y ago
      > At some point in the past we had a lot more Mercury-to-Mars-sized things floating around than we do now. How long ago the last one got eliminated is anyone's guess, but it was almost certainly a few billion years. The last one hasn't been eliminated - we still have Mercury and Mars. You probably don't think of it that way because we think of the existing planets as constants, not variables.

fbdab103 4y ago

>What they find is that after switching off general relativity the Solar System goes unstable shortly thereafter. Not my field, and I only glanced at the figures, but I think "shortly thereafter" is something only a cosmologist could say without blushing. Unless I completely bungled the meaning (very plausible), the paper is using time on the scale of billions of years.

lloeki 4y ago
I guess the timescale was picked up to match the expected end of Sol's main sequence (in ~5 billion years) and its growth into a planet-engulfing red giant, in which case continuing with the model beyond the next order of magnitude becomes unrealistic. IIUC the instability time scatter plot shows that GR basically stabilises our local N body problem by one to two orders of magnitude in time scale (10^8~10^8.5 vs 10^9~10^10), IOW giving a 900~9000Myr extra vs being derailed by a Mercury-Venus collision in ~100Myr, which would indeed comparatively be "shortly thereafter" at these timescales. I did chuckle at the phrasing though. (Disclaimer: not my field either, so I may be 10^10 wrong)
antognini 4y ago
Hah, fair. As an astronomer I don't really blink when someone says that 100 million years is a short time period.

towei4uo34i3 4y ago

Neat. I was half-disappointed that they didn't use scmutils (like Sussman & Wisdom) : (

causi 4y ago

So the stability of the Solar System is highly dependent on general relativity. That seems a bit misleading. If you have a complex system that reaches a measure of stability over a large timescale and then change any of the underlying rules, it's going to become unstable. In this scenario there's nothing special about special relativity, it just happens to be the rules they messed with.

infogulch 4y ago
That's a fair criticism. If a dynamical system is stable under one model, it's not that surprising if suddenly swapping out the model causes an instability. Basically, different models have different stability islands, if you would. But the question remains, how dependent on GR is the long term stability of an N-body system in general? Here's an experimental idea: create a "random N-body system" generator, and compare what % of systems are stable under Newtonian vs Einsteinian physics models.
- raattgift 4y ago
  > in general That's too broad to answer. Let's narrow to our solar system, or a close approximation, first. Below, I'll step up to more complicated arrangements, and binary black holes. These are only three or four families of (regions of) general curved spacetime; there is a very large infinity of other families one could reasonably associate with "in general". In a (model) solar system, there is a large central mass and several other objects with extreme mass ratios to the sun. There are interesting secular resonances among Mercury, Venus, and Jupiter, and between Earth and Mars, where that means that from time to time (over many orbits), the precessions of the near-to-the-sun parts of the planets' orbits match. These resonances may increase the eccentricity of the smaller mass's orbit, which can in extremis yeet the small body out of the solar system, or cause a collision between planets (e.g. Mercury's orbit may near aphelion cross Venus's orbit). For the Mercury-[Venus-]Jupiter the closeness of Mercury to the sun tends to break up the resonance enough to significantly stabilize the shape of Mercury's orbit. Any sort of slow-down on the inner body when it and heavier outer bodies are relatively close together with the sun is liable to suffice, and that's what the authors of the link at the top argue what we get with (good approximations of) GR. (The approximations used by the authors are a post-Newtonian expansion <https://en.wikipedia.org/wiki/Post-Newtonian_expansion https://en.wikipedia.org/wiki/Post-Newtonian_expansion> and numerical methods). Very roughly, thanks to the large central mass and the very different distances of the planets involved, the outer body rushes ahead or equivalently the inner body lags behind, which avoids stabilizing the resonance. Many -- possibly even most -- stars are in binaries, rather than singletons like our sun. Planetary orbits in a binary (or triple) star system are likely to be dramatically different. In binaries, the width and mass-ratio between the partners are relevant quantities. Triples can be arranged in all sorts of ways. PSR J0337+17 is one known arrangement <https://www.youtube.com/watch?v=oDgfqq_W_uM https://www.youtube.com/watch?v=oDgfqq_W_uM>. PSR B1620-26, a pulsar-white dwarf binary, has at least one planet. I have only weak intuitions about what Jupiter or Earth mass bodies would do in such systems, or even how to select a reasonably astrophysical set of initial orbital values. (There are known circumbinary planets. See <https://en.wikipedia.org/wiki/Circumbinary_planet https://en.wikipedia.org/wiki/Circumbinary_planet> and <https://sci-hub.ru/10.1007/978-90-481-8687-7 https://sci-hub.ru/10.1007/978-90-481-8687-7> in which Chapter 9 details how these can be simulated). It is not too fanciful however to suppose that periastrons could be close enough that post-Newtonian effects are non-negligible, even if the stellar masses are non-compact. That doesn't say much about whether secular resonances (in the sense above) are likely in such systems. I have no idea, but I'd guess they aren't forbidden. > compare what % of systems are stable under Newtonian vs Einsteinian [gravitation] That's what the authors do in their paper <https://arxiv.org/abs/2303.05567 https://arxiv.org/abs/2303.05567>, although "systems" here is a simplified model of the solar system (they discuss several simplifications and their justifications: the oblateness of the sun and the presence of moons are probably interesting "future work" but are most likely not going to result in large corrections see their §3.2). For non-isolated systems, interactions with the environment can magnify whether these properties drive dynamical stabilization (merger) or instability (fly apart). The authors in their other fresh paper even more freshly summarized at <https://astrobites.org/2023/03/14/chaos-planets-future-of-the-solar-system/ https://astrobites.org/2023/03/14/chaos-planets-future-of-th...> discuss how "environmental events" (nearby stars and their potential to approach our solar system) might lead to e.g. collisions between Earh and Mars, or an ejection of one or more planets into deep space. Astrobites has also freshly summarized another "environment can change orbits" (for 2-body + dusty environment) at <https://astrobites.org/2023/03/13/will-it-merge-investigating-how-gas-disks-can-determine-the-future-of-a-binary-black-hole-system/ https://astrobites.org/2023/03/13/will-it-merge-investigatin...>. ("Dust" in the GR sense of <https://en.wikipedia.org/wiki/Dust_solution https://en.wikipedia.org/wiki/Dust_solution>, rather than in the sense of fine particles of e.g. chalk that allegedly accumulate on sedentary GR theorists). > Here's an experimental idea Been done (and improving) for many decades. See for example Fig. 1 in <https://arxiv.org/abs/1105.1082v1 https://arxiv.org/abs/1105.1082v1>.

AdamH12113 4y ago

Since Mercury is the closest planet to the sun, wouldn’t it need the most delta-v to escape the solar system? What about it makes it the most likely planet to be ejected?

jessaustin 4y ago
It is less massive than the other planets. Momentum is conserved, so any escape scenario would see at least one other planet with a smaller orbit.
bmitc 4y ago
The solar system is a chaotic, dynamical, and n-body system though, so the 1 or 2-body problems involved in delta-v calculations are much more simple. In addition, Mercury's mass is low, relatively speaking.