
Signature of a resonance transition between Mars and Earth - shawndumas
http://news.wisc.edu/from-rocks-in-colorado-evidence-of-a-chaotic-solar-system/
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antognini
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.

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pavel_lishin
> _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."

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antognini
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.

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

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imglorp
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...](http://www.wolframalpha.com/input/?i=G+*+6e24+kg+*+6e23kg+%2F+\(7e19m\)%5E2)

~~~
cmsmith
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.

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

~~~
antognini
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.

~~~
quantumhobbit
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.

~~~
antognini
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.)

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ChuckMcM
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.

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AnimalMuppet
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?

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pavel_lishin
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!

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

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yohann305
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?

~~~
Udo
> _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.

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Sniffnoy
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.

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sp332
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?

~~~
AnimalMuppet
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.

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santoriv
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?

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

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sebringj
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?

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

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

