Signature of a resonance transition between Mars and Earth | Hacker News Reader

Signature of a resonance transition between Mars and Earth

news.wisc.edu

63 pointsshawndumas31 comments

Orbital resonances are a powerful phenomenon over a long enough time. This article doesn't mention it, but Mars's rotational axis is also chaotic. The whole planet can change its axis of rotation over the course of a few million years. It is likely that something similar happened to Mercury, though tidal friction has slowed its rotation enough that it's unlikely to occur anymore. The only reason this doesn't happen to the Earth is that the presence of the Moon stabilizes our rotation.

Also, there is a few percent chance that Mercury will be ejected from the Solar System due to orbital resonances before the Sun dies. A general principle of planetary dynamics is that systems are only barely stable --- they are stable only over timescales of approximately their lifetime. Then they will suddenly go through a period of chaos, only to settle into a slightly more stable state and start the whole process over again, with a longer timescale.

> A general principle of planetary dynamics is that systems are only barely stable --- they are stable only over timescales of approximately their lifetime

I think I might be misunderstanding what you wrote, because it sounds tautological to me - "Systems are only stable as long as they remain stable systems."

I find it a bit counterintuitive. After all, the natural timescale for planetary dynamics should be the orbital period --- i.e., a few years. So one might think that if the system is unstable, it will dissociate within a few years. If it doesn't do that, then it should be stable for all time. But instead the next system takes 10 years to fall apart. And the next one takes 100 years, and then 1000 years, and so on. And eventually these systems (whose natural timescales are still years) take billions of years to fall apart.

You would think that if it is unstable, then it should reorganize itself into a system that is stable for all time. It's a little bit odd that every time the system reorganizes itself, it is only a little more stable than it was when it started. Somehow, planetary systems are always just sort of end up teetering on the edge of stability.

That is interesting - it seems counter-intuitive to me that the periods of apparent stability would tend to increase in duration over time.

So they seem to be implying a gravitational interaction between Earth and Mars. Out of curiosity I wanted to see roughly what kind of forces we're talking about at closest approach. (Edit: including feedback below, thanks)

    r   1e11 m
    Me  6e24 kg
    Mm  6e23 kg
    G = 6e-11 m^3 kg^-1 s^-2

    F ~~ GMeMm/r^2 = 6e-11 * 6e24 * 6e23 / (1e11)^2 
      ~~ 2e16 N

http://www.wolframalpha.com/input/?i=G+*+6e24+kg+*+6e23kg+%2...

Only thing that might be off is the radius there, as it'll vary based on the phase that each planet is in it's orbit, which will make it go even lower at points.

Also WFA will do the units too, http://www.wolframalpha.com/input/?i=G+*+6e24+kg+*+6e23kg+%2...

> What am I missing?

Resonance over a few million years.

Okay, so does that mean the resonance has damped over the years or built? Even if I'm off by 3 oom, it's still less force than 1kN between planets, hardly enough to influence our geology.

Your distance is off by quite a bit (should be ~1e11 m at closest approach).

The actual force is closer to 10^16 N. Which is big, but 10^7 weaker than the earth-sun interaction. But the sun has to move the earth by a couple AU per year whereas Mars has had a couple billion years to move it by the same amount.

You got the distance wrong. The minimum distance the two planets can have on their orbits is 55 million km. The force between the two is of the order 1e15 N.

The value `r` above is off by a factor of 10^9. It should be 0.5 AU or 7.48x10^10 meters:

http://www.wolframalpha.com/input/?i=distance+between+Mars+a...

The current gravitational force between Mars and Earth is 2.832x10^15 N:

http://www.wolframalpha.com/input/?i=(gravitational+constant...

For comparison, the current gravitational force between the Sun and Earth is 3.614x10^22 N:

https://www.wolframalpha.com/input/?i=(gravitational+constan...

P.S. My favorite Wolfram Alpha feature is being able to use natural language descriptions of various quantities!

Chaotic movement towards the end of simulation looks suspiciously like aggregation of computational errors and loss of modeling accuracy.

I haven't read their paper, but the usual way to test the accuracy of your N-body simulation is to check to see how well energy is conserved. If your simulation is going crazy due to numerical errors, this will be reflected in the energy changing wildly. If the change in energy is very small, it is likely that the chaos you're seeing is real.

Yup. For more accuracy, you can also vary the timestep by small amounts and rerun the simulation. If they give the same results you assume that numerical errors aren't a problem.

Depending on the integration scheme used, the errors sometimes bias in the direction of adding energy, so normally numerical errors would look like all the planets gaining velocity and leaving orbit. "Blowing up" the simulation if you will. The wiggles in orbits of the video look like a legit chaotic system to me.

One thing to note, though, is that if the two calculations match, then that's great and you can trust the results. But even if they don't agree, you still might be able to trust the results. Often these sorts of long-term simulations are only done in a statistical way. You can't trust the results of any individual simulation due to numerical uncertainties, but you can trust the aggregate results of a large set of simulations all run with slightly different initializations. (So, you could run many long term simulations of the Solar System to conclude that there is a 3% chance that Mercury will be ejected.)

This is an excellent piece of work and one that helps give some solidity to the notion that the stability of our situation on the planet only seems stable because we have only been recording (and hence reliably remembering) how things were for the last 2000 years or so. Suggesting once again that being able to live on different planets in the same system and to easily move between them would be an excellent survival tactic.

Off topic, but: Did anyone else find it annoying that the actual research is about rocks in Colorado, but the picture is from Big Bend in Texas?

I like the crash-porn at the end that preserves our landmasses exactly.

And say what you will about the instability of the solar system, but if orbits start coinciding, it might make interplanetary travel quite a bit cheaper!

That is actually only about a third of the way down. There are more details about depositions and ancient oceans below.

if planets revolving our sun can somehow collide with eachother, we should be able to see the same phenomenom happening in other star systems. Do we have evidence of it?

> if planets revolving our sun can somehow collide with eachother

It's not "somehow", it's only a matter of time until something happens in most star systems. They are only stable over human-relevant time spans, they're not static. Every star system is the result of the evolution-like process of its formation. What we see as the result of that process is literally only there because it survived long enough for us to see it. These systems do change over time. Small deviations add up, some are subject to cumulative destabilizing factors (such as the Earth-Moon system), and sometimes it's just due to a rare event occurring.

> we should be able to see the same phenomenom happening in other star systems. Do we have evidence of it?

Oh yes. We're seeing extrasolar planets that we think have moved significantly during their life (mostly inwards, because our detection methods favor those). And sometimes we see dust clouds that are the result of planets colliding.

Again, there is nothing new or surprising here. We haven't thought of star systems as static and perfect for a long time.

> Do we have evidence of it?

The Moon may be evidence of it. https://en.wikipedia.org/wiki/Origin_of_the_Moon

The abundance of hot Jupiters is probably the most vivid example that planetary migration is ubiquitous. Jupiter-sized planets need to form far away from their host stars, but many of them eventually end up very close, much closer than Mercury is to our Sun.

Well, after a billion years the sun will be too hot for life on Earth to survive anyway, so it seems a little pointless to worry about orbit destabilization at that point; if we're somehow still around, we'll have to have moved off-planet anyway. That or taken control of the planet's orbit (to move it away from the sun), in which case we probably have the tools to handle the problem regardless.

How would radioisotopic dating work here? All the clay is coming from the same places upstream and being deposited in layers. Same for the calcium carbonate. So just rearranging the material shouldn't change the decay rate, right? What would be radioactively different from one layer to another?

Seems to me that, when dating the clay, you're dating the formation the clay eroded from (unless whatever radioactive isotope you're using escapes out of small rock particles). Calcium carbonate, on the other hand, as the article said, is produced by life forms - but from what material? Well, the "carbonate" could be atmospheric, but the calcium isn't. It also could be dating its origin, not its deposition.

Hmmmm.... So if you were immortal and wanted to ditch Earth, it would be best to go to a supercool dwarf with only 1 planet? Otherwise you might get pulverized before the end of the dwarf's lifecycle?

A rogue planet headed for intergalactic space might be a better bet.

This would be really scary if it was relatively eminent, but its like so far away that we would have 5th dimensional technology if we survived as a species by then and could slip into different parallel dimensions where issues don't happen or way more likely before would have already populated many exoplanets rendering this not even an issue. Did I mention I don't know what the hell I'm talking about?

The 5th dimension? You might be under the influence of Dr. Chaotica.

Probably. I shouldn't stick my nose in a subject I have no business to comment on. I'll keep on programming. :)

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