Some 15 years ago, a new phrase erupted onto the scientific stage. Once coined,
a flurry of media interest sought to popularise the new science of "chaos
theory". Top selling books were doing their best to explain it, whilst
artists and publishers alike marketed the exotic imagery of fractal art, the
iconography of this new age of enlightenment.
The word chaos is now an integral part of new-speak along with holes in the
ozone layer, global warming, the butterfly effect and catastrophe theory (to
name but a few) and they all seem to have become jumbled together into a series
of meaningful clichés uttered knowingly by the cognoscenti.
But what does it all mean ? What is chaos theory about and how does it really
affect our picture of the Universe we inhabit ?
To answer this, let us place ourselves in the position of a prehistoric cave
dweller (if at all possible!): This short lived individual would undoubtedly
agree that all around was chaos, in the sense that events were on the whole
irregular and disordered. Only a few regular occurrences could be depended upon,
the most obvious being the motion of the Sun and stars during the day/night
and over the course of a year, the rise and fall of tides and the changing appearance
of the Moon during the month.
As civilisations developed, this picture improved little. Individuals and nations
sought to impose order upon the chaos, probably the most successful being the
Greeks and Romans, but in the end even these great civilisations were torn apart
by internal instability.
The Renaissance period saw a rise in natural philosophy that drew on the inspiration
of Greek thinkers, but also nurtured the spirit of empiricism - actually observing
nature and seeking to explain it in terms of a consistent model that could be
used to predict events. This process was the start of scientific enquiry. Much
of the apparent order was mathematically devised and architecturally imposed,
yet rarely reflected in the world around.
Just as prehistoric man recognised the predictability of the skies, so too the
new seekers after truth turned their attention to the heavens. The ancient cosmos
of Sun, Moon and five planets had been known for thousands of years, and the
motions of these bodies against the fixed stars charted with some precision
by the C16th . The dominant ideology was that of Ptolemaeus and his epicyclic
theory.
In 1504 at the age of 31, Niklas Koppernigk (Copernicus) observed a conjunction of all 5 planets and the Moon in Cancer and noticed that the observed positions differed substantially from those predicted by epicyclic theory. Applying Occam's Razor to the number of alternatives, he came to favour the heliocentric model and circulated his Commentariolus In 1643 he published a synthesis of all his work - de Revolutionibus.
Between 1576 and 1596, Tycho Brahë made detailed observations of stars and planets from his observatory near Copenhagen. These precise catalogues were not enough to convince him that Copernican theory was entirely correct, but it did provide further ammunition for the revolution.
When Tycho died in 1601, Johannes Kepler, his assistant, inherited all his observations and was sure that the motions of the solar system were governed by hidden regularities - the "harmony of the spheres". His major contribution was to modify the circular orbits of Copernicus into elliptical orbits with the Sun at one focus. He published the Harmony of Worlds in 1619, outlining his three Laws of Planetary Motion.
In 1609, Galileo Galilei turned his newly acquired telescope on the heavens and made three significant discoveries that confirmed his own belief in the Copernican system, namely that Venus shows phases, that the Moon has mountains and that Jupiter has its own mini "solar system" of 4 moons.
It took the genius of Isaac Newton to synthesise these ideas and observations into a fundamental theory. He published the Principia Mathematica in 1687, outlining his Theory of Universal Gravitation and his Three Laws of Motion. This theory explained Kepler's Laws, and with the help of his "infinitesimal calculus" (co-discovered with Leibnitz) was supreme in predicting planetary motions (with the exception of Mercury - a fact that required Albert Einstein and General Relativity to clear up some 220 years later).
A curious relationship was discovered by the German astronomer Johann Titius and popularised by his colleague Johann Bode in 1772 in which the average distances of the planets from the Sun can be approximated to a simple geometrical progression - known as Bode's Rule
With the foundations of classical science laid firmly by Newton the confidence
was gained to analyse nature on every level - to reduce it to some simple causal
relationship or equation that would explain all the complex behaviour around
us. Underlying this revolution in reductionist thinking was a belief in determinism
i.e. that every event was caused by - and depended directly on the event immediately
before it, and that there was a chain of causality threading the world together.
Even seemingly random happenings had causes which were undetectable (physical
or spiritual).
Towards the end of the C18th the confidence in the ability to describe
the Universe precisely in terms of a few simple mathematical relationships could
be summed up in the philosophy that "All clouds are clocks!" The logical
sequitteur of this world-view was that if one could only know the positions
and motions of all the particles in the egg and sperm that would become Mozart,
and the environmental forces acting throughout his life one could, in theory,
predict the Requiem in D Minor! The principle exponent of this attitude was
a French mathematician, Pierre-Simon de Laplace who declared in 1773 that :
"All the effects of Nature are only the mathematical consequences of a small number of immutable laws."
He appeared to be vindicated in 1781 when William Herschel discovered Uranus,
and later on in 1845 when Neptune's position was calculated by John Couch-Adams
and Urbain LeVerrier, the planet actually being discovered a year later at the
Berlin observatory.
It seemed that the Universe, especially the solar system was a great clock driven
by the grinding wheels of Newtonian mechanics.
There were, however, a few dissenters to this optimistic scheme who argued
persuasively that just knowing enough about the state of even a simple system
was not enough to predict its evolution - as any one has bet on the roll of
a die, or done the National Lottery will know! In particular, a competition
based on questions proposed by the mathematician Karl Weierstraß in 1889
offered a prize to anyone who could furnish a definite proof that the solar
system was stable for all time. Little did the organisers realise that in searching
for a formal solution to this problem, the seeds of a new uncertainty were being
sown that would throw serious doubt on the clockwork universe model.
In fact, it was a pincer movement, for at the turn of the C20th,
Max Planck and Werner Heisenberg laid the foundation for a whole new way of
describing the microscopic world, not in terms of classical particles with precise
positions and velocities, but as a collection of nebulous probability waves
that existed in multifarious states and would only yield information about their
velocities at the expense of their location. The Quantum Theory is supremely
successful in its predictive ability and sets a fundamental limit on what it
is possible to know in our Universe. It is still a theory based on determinism,
but we are forced into ignorance of the very factors that would allow us to
predict a precise future - we can only deal in probabilities. It seems that
now "All clocks are clouds!".
Modern science is untroubled by this picture and has absorbed the quantum world
as a fundamental foundation
Classical (Newtonian) dynamics was generally held to be predictable by comparison, provided one had enough information to start with - and enough computing power ! It is not surprising that it was only in the last 25years that such computing power has been available - and shown that classical dynamics has a few surprises up its sleeve.
Consider a very simple mechanical system - an epitome of order and regularity
- the humble pendulum. Once swinging it will trace out a repeated path that
slowly diminishes in amplitude, but maintains a constant period - the ideal
device to regulate a clock (as Galileo discovered). We may describe its motion
in terms of a simple equation so that at any time in the future, provided we
know its position and velocity to start with, we can compute its position at
any time in the future long before it actually gets there. We don't have to
know its initial position too accurately either, because if we start with a
small error, that error will only grow at a linear rate that depends on the
accuracy of the calculator. If we start the pendulum swinging from one point
and follow its evolution, then start from a point close to that original point,
the motions would be very similar.
It is possible to represent the motion on a phase space diagram where we plot
position against velocity and get a closed orbit that spirals in towards an
attractor or point of stability. Two initial positions close together would
give two similar orbits in phase space very close together.
This very simple system changes if we oscillate the point of suspension or
use a magnetic bob and magnets in the base. In terms of the forces involved,
the system has not increased in complexity by much, but in terms of the behaviour
of the system, it has become entirely unpredictable. If we try to plot a phase
space diagram for this system, parts of it degenerate into areas of irregularity
- chaotic zones.
If we try to reproduce the same motion by starting at the same place, we get
a different evolution every time. The behaviour is Sensitively Dependent on
Initial Conditions - SDIC (or SIC for short!)
Any tiny difference in initial conditions is amplified and grows exponentially
as the motion progresses in its tortuous path through phase space. The rate
of divergence is characterised by something called the Liapunov time.
There is no simple equation we can program into a computer and use to compute
the position at any time in the future from a set of starting conditions. We
have to constantly work out the new forces acting on the bob and use those to
predict what will happen a short time later - and here's the rub - it is impossible
for any computer to work out the orbit faster than the motion itself unfurls.
This is really the best definition of chaotic or SIC behaviour - It is its own
fastest computer !
So what is chaos?
It is essentially deterministic but wholly unpredictable behaviour arising out
of simple systems. Chaos is a synonym for random and is indistinguishable from
truly random behaviour (if such exists)
This doesn't mean it only occurs in simple systems - it occurs everywhere; from
turbulence in fluid flow to weather systems on ours and other planets, from
the growth of a snowflake to waves breaking on a shore, the flicker of a camp
fire flame to the serene motions of the solar system in the skies above.
The cyclical variations of the Moon's shape must have had a fascination for
early peoples. Their reaction to the phenomenon of an eclipse must have prompted
certain groups of people to study eclipse cycles with the aim of predicting
them. In fact, there is evidence to suggest that before any stones were erected
at Stonehenge (c2500 BC), a series of post holes were used as sighting lines
to monitor the Moon's movements over extended periods of time.
Compared to the Sun, the apparent motion of our satellite as seen from Earth
is complex. The position of most northerly moonset wanders up and down the horizon
with a period of 186 years - a period identified by the ancient astronomer/priests
- and known as a saros cycle.
The main reason for this is that the Moon's orbit is tilted at 5.15° to
the plane of the ecliptic. It takes roughly 275 days to make one anticlockwise
circuit of this platform, but the whole platform rotates clockwise with a period
of 186 years.
If this were all the Moon's motion depended on, then life would be simple. The
earliest observations of the Babylonians and Greeks showed that the Moon appeared
to speed up at certain parts of its orbit, yet slow down at others, giving rise
to librations in latitude (±6.5°) as well as longitude (±7.5°).
Replacing the Ptolemaic epicycles with ellipses did little to improve the predictions
of C16th astronomers. The whole industry of publishing lunar almanacs
was riddled with discrepancies and inconsistencies. Even the great astrologer/mathematicians
such as Tycho and Kepler made embarrassing errors in the timing of eclipses.
It was Kepler who first proposed the notion that the Earth/Moon system was not
isolated, but intricately linked with the influence of the Sun.
Newton had considerable problems applying his theory to the Moon. In 1695 he
abandoned the task, admitting failure and went on to manage the Royal Mint!
Newton was followed by a host of esteemed mathematicians, most notably Leonhard
Euler, Alexis Claude Clairaut and Jean le Rond d'Alembert, the last two ended
up in acrimonious public dispute.
Theory was refined and predictions became increasingly accurate. Building on
the work of Joseph Louis Lagrange, Pierre-Simon de Laplace eventually succeeded
in predicting the Moon's position to within 0.5 arc min.
The success of the Apollo programme really depends on the American naval astronomer
George William Hill who discovered a different, more efficient approach to calculating
lunar orbits than Laplace. He identified a long term periodic trend that serves
to increase the Earth-Moon distance, but although the theory was refined, it
was not absolutely accurate.
Why should this be such a problem ?
The essence lies in the dynamics of many body systems.
Kepler's Laws are an expression of the solutions to a specific problem in orbital
mechanics - the two body problem. Essentially, for any two gravitating "point
masses", all the orbits will be conic sections and will be "bound"
or "unbound" depending on the initial energy of the system. It turns
out that under these conditions a series of mathematical solutions can be worked
out that will describe the orbit precisely for all time.
If we now increase the number of interacting bodies by one, there is no general
analytical solution to the three body problem.
Apart from a few very specific combinations of masses, the only way to work
out an orbit is to take a starting position, calculate all the forces acting
on the orbiting body at that instant, allow the body to be accelerated for a
certain time and find its new position. Such a process is called integration
and there are many ways of increasing its accuracy - the most obvious is to
reduce the time step. The calculated orbits are only approximations and depend
on how accurately the starting conditions are described together with the precision
of the calculator. Even simple computations for three body systems (e.g. the
motion of a small planet in a binary star system) produce wildly fluctuating
orbits that have all the hallmarks of SIC behaviour.
It is the fact that the Moon is influenced by the Sun as well as the Earth that
produces elements of chaos in its motion It must be remembered that we are looking
at a two body system that is perturbed by a third, rather than dominated by
it, so the departure from predictability is not that great - it is constrained
chaos. This mixture of predictability and randomness is characteristic of much
of the motion in the solar system.
Only occasionally does chaotic behaviour become the dominant partner. One such
example resides in the Saturnian system.
Discovered in 1848, this small satellite of Saturn orbits once every 213 days
just outside Titan's orbit. Its small size ( <400km ) meant that until the
Voyager II flyby in 1981, very little was known about it. Voyager images showed
a deformed potato shape 380 x 290 x 230km. These same images showed its inclination
changing.
In 1984, Jack Wisdom, Stanton Peale and Francois Mignard had predicted a tumbling
orbit as a result of the combined tugs of Saturn and Titan.
In 1987, James Klavetter attempted to gather enough data to prove that Hyperion
was in a chaotic orbit. He aimed to observe the moon for 45 orbits (91 days)
using Cerro Tololo, Lowell Observatory (Flagstaff, Arizona) and McGraw Hill
2.4m nearby. Due to the glare of Saturn, inclement weather and equipment problems,
only the McGraw Hill data was usable. After sky glow and background stars were
subtracted the light curve was plotted and no periodic function would fit the
data, despite the strong variations in brightness. To consolidate this hypothesis,
Klavetter tried to model Hyperion's dynamics by assuming it was a smooth ellipsoid
under the influence of Saturn and Titan and working backwards from his observations
to find a set of initial conditions. It is impossible to fit a calculated orbit
to it (chaos precludes it) but Klavetter's observations indicate the moon is
uniform in density and is probably the remains of a larger body that fragmented
long ago.
Why is it chaotic ?
Any asymmetric satellite with initial spin will interact tidally with its parent
body thus losing energy and slowing down to become "phase-locked".
All of the smaller satellites we observe are asymmetric and the process of formation
lends asymmetry to the larger ones. Most major satellites in the solar system
have this 1:1 resonance between their rotation rates and orbital periods (e.g.
the Moon). Highly asymmetrical satellites will end up spinning about their short
axis with their long axis pointed towards the planet. Hyperion is highly asymmetric
and should have become locked quickly since there is more gravitational "leverage"
on it. However as the satellite slows down and approaches this 1:1 resonance
it enters a chaotic region where its axis of rotation skews violently - it starts
to tumble. It seems that all irregular satellites have gone through this process
and come out of it again because the chaotic zone is not that wide, but what
has conspired to maintain Hyperion's chaotic behaviour is the 4:3 resonance
between its orbit and that of Titan. This has extended the chaotic region to
an area so vast that the chances of the satellite ever passing to an island
of stability is minimal. It seems destined to tumble forever !
Phobos and Deimos, the twin irregular moons of Mars could have tumbled chaotically
for between 10 and 100 million years before being locked into their regular
orbits.
Neptune's satellite Nereid may also have gone through a similar stage (it is
about the same size as Hyperion, but has a highly elliptical orbit).
Although the features of Miranda indicate an active geological history, the
wide range of ages of these features reveal it is unlikely that its period of
chaotic tumbling had much of a role to play in sculpting its bizarre surface.
These findings have important applications in the satellite industry. Many satellites launched into Earth orbit are elongated or irregular and are spinning . Since they are small they respond to fluctuations in the strength of the Earth's gravitational field caused by density variations. It was found fairly early on that any satellite in a geo-stationary orbit will tend to drift and eventually come to rest over the Indian Ocean due to a mass concentration there. The combination of these and other factors mean that there are many orbits that are unstable and can induce bouts of minor chaos. The detailed mathematical modelling of some of these orbits has been a persistent headache for engineers - in particular the "critical inclination" of 63°. It came as a shock when the USSR successfully launched satellites at this angle and their orbits proved stable!
Following the hunt for the "missing planet" intimated by Bode's Rule,
the first of the minor planets or asteroids was discovered in 1801 by Giuseppe
Piazzi - 1 Ceres. Since then over 5000 of these bodies have been catalogued
ranging in size from a few km to 1020 km, and an estimated 100 000 observable
ones remain uncharted. Most of these inhabit a broad belt between Mars and Jupiter.
The combined mass of all these fragments is only 5% that of the Moon, so lumped
together they would make a body 1500km in diameter.
Other examples reside at the Lagrangian points of Jupiter's orbit (the Trojan
asteroids), whilst others also occur inside Earth's orbit (Aten), outside
its orbit (Amor) or more importantly, orbits that cross that of Earth
(Apollo).
Despite the vast numbers of asteroids moving in elliptical orbits, close approaches
are very rare - on average they are several million km apart. However they are
in a region where a gravitational tug-o-war is going on between the Sun and
Jupiter. This leads to some fascinating dynamics.
In 1857, Daniel Kirkwood (of Indiana University) made a study of 50 known asteroid
orbits. When he plotted the number of asteroids against their distance from
the Sun (or more correctly their semi-major axes) he noticed certain perplexing
gaps devoid of asteroids. These have come to be known as Kirkwood gaps. There
were also clumps of asteroids at other positions.
An analysis of these gaps showed that they corresponded to simple fractions
of Jupiter's orbital period - they were resonances. At the time no theory could
adequately explain the gaps as a result of gravitational interactions, and certain
astronomers believed the gaps were present at the inception of the solar system.
In the 1970s astronomers attempted to integrate asteroid orbits over 10 000
yrs. Both the unwieldy nature of the problem and the processing power of their
computers set a limit on what they could deduce. This spurred Jack Wisdom, a
graduate at Caltech to attempt to streamline the computations to reach further
into the future. When he ran a simulation of asteroid orbits in the vicinity
of the 3:1 resonance with Jupiter's orbit over a period of 100 000 yrs he discovered
chaos. Sudden large changes in the eccentricity of orbits appeared almost at
random. If these changes were great enough to place the asteroid in a planet-crossing
orbit, then that asteroid would be "swept up" by the Earth or Mars.
Here was a hitherto unknown mechanism to account for the gaps. The big question
was - did this happen as a result of the computing system used to model the
behaviour, or was it inherent in nature ?
The computations have been refined to minimise errors, and the general agreement
is that the effect is there in nature - as witnessed by Phobos and Deimos and
the regular new supply of Earth crossing asteroids.
Although it is impossible to predict exactly where an asteroid will be 200 000
yrs into the future, the likelihood of it entering a highly elliptical, planet-crossing
orbit is better understood.
Detailed investigations of the various zones in the asteroid belt have also
revealed large areas of stability and order accounting for the clumping of asteroids
at certain distances, but there are still some questions that remain unanswered,
for example there is a gap at the 2:1 resonance, and it is a chaotic zone, but
what is there to sweep up any asteroids that become highly eccentric ? There
are also examples of asteroids exhibiting chaotic behaviour which follow confined
orbits - examples of "stable chaos".
With the dawning realisation that modern computing power could reveal insights
into many body behaviour over long time scales, the solar system itself came
under scrutiny.
Newton had applied his new Laws to the then known solar system of Sun and six
planets. He found disturbing evidence that it was unstable and needed to be
periodically reset to preserve the "integrity of God's work".
Laplace did considerable work on the celestial mechanics of the solar system
between 1799 and 1825 and was convinced of its regularity.
Other mathematicians were not so sure, principal amongst them was Henri Poincaré‚
He demonstrated that there is no short-cut or magical formula for making predictions
of the positions of multi-body systems. Typically the mathematical series used
to model them diverge. It is possible to obtain an approximation using the first
few terms of the series (as had been done up to then for the Moon). In 1903
he published a radically different approach that sought to characterise an orbit's
evolution in phase space. This showed how the solutions to a differential equation
flowed for different starting conditions. By taking a cross-section of that
space he could see if an orbit was periodic, quasi-periodic or irregular. He
found that trajectories with very similar starting points can diverge rapidly
in this phase space and appear to wander all over the place. This is the signature
of dynamical chaos. The motion is governed by a fractal attractor.
This foundation led Andrei Kolmogorov in 1954 to tackle certain aspects of the
behaviour of orbits in phase space.
In 1963 Vladimir I Arnol'd developed Poincaré's work to show that provided
planets in a solar system are small, lie close to one plane and move in near
circles, then that system is stable. This is one result of the KAM theory (named
after Kolmogorov, Arnol'd and Jürgen Moser).
But is our solar system like this ?
The only real way to find out is by numerical experiment. We need to perform
a long time integration of all 9 major bodies over billions of years (the solar
system has already been around for 4.6 billion years and the Sun will continue
to shine for at least another 5 billion years). This requires very powerful
computers and efficient mathematical techniques to perform these integrations
with the required degree of accuracy. It also requires accurate determinations
of the planets' masses and current orbits. Using a combination of astrometry,
radar ranging and data from interplanetary probes (most notably the Voyagers)
these have been determined to better than 0.001 % (with the exception of Pluto,
whose mass is only known to 0.5%).
The history of such integrations spans the last 40 years. Many follow only the five outer planets since:
Vector or parallel computers are of little use yet in these integrations, in
fact the most successful strategy has been to purpose build machines wholly
dedicated to the task.
The first of such machines was built by Gerald Sussman at MIT in 1984 He called
it the digital orrery. In collaboration with Jack Wisdom, it performed
its first integration for the outer planets in 1988, reaching 100 million years
forward and back in time. The machine churned out data, not on the positions
of the planets, but on variables connected with the orbit (period, eccentricity,
inclination etc). When these were displayed as power spectra, the intricacy
of planetary dynamics was illuminated and spurred on a drive to an even longer
integration lasting 5 months and covering 845 million years!
The findings of these, and subsequent experiments using more powerful machines
(e.g. the supercomputer toolkit), have illuminated the complexity of the solar
system's evolution.
Just using the gravitational interactions of the planets is inaccurate over
these timescales and recent integrations have sought to correct for errors caused
by:
At roughly the same time as these massive integrations were taking place,
an astrophysicist by the name of Jacques Laskar developed a branch of celestial
mechanics called secular perturbation theory, originally proposed by
Laplace.
The essence of this is to smooth out periodic and quasi-periodic wiggles in
a planet's orbit, leaving only long term trends. What Laskar found (and published
in Nature in 1989) is that most of the members of the solar system follow chaotic
trajectories in the sense that a slight change in initial conditions leads to
an exponential divergence in orbital parameters with lyapunov times between
4 and 25 million years.
In 1990 Thomas Quinn, Martin Duncan and Scott Tremaine at Toronto University
refined their own methods for computing planetary orbits over long time scales
and backed up both Laskar's and Wisdom's findings. This was important since
they had all used different physical models and procedures, yet identified similar
trends.
Our current understanding of the behaviour of each member of the solar system is as follows:
This has large and irregular variations of both its orbital inclination and
its eccentricity over 100 million years.
Laskar found a small but non-zero chance that it could be ejected or collide
with Venus in less than 5 billion yrs.
Small variations in eccentricity and tilt. Its past may have been far more chaotic. The 243d retrograde rotation is unique in the solar system and needs explaining.
The eccentricity of the orbit varies chaotically from 0 to 10% over 100 million yrs. The tilt stays around 23° since it is stabilised by the Moon's orbit and the fact that the precession rate is not slow enough to resonate with any other long term variations in the solar system . When the Earth/Moon distance increases to 68Re (in a few billion yrs) it will enter a chaotic regime giving rise to possible tilt angles of 60° (2° can trigger an ice age !)
This planet shows wildly varying eccentricity (it already has a more distorted orbit than other terrestrial planets). Its wild gyrations and vibrations have a profound effect on its axis of rotation. This can change dramatically by as much as 60° in only a few million years. This may explain the loss of thick atmosphere and surface water that once existed on the Red Planet
Apart from the chaotic fluid dynamics responsible for its ever changing cloud features, this giant of the solar system has revealed a chaotic, increasing orbital motion over 108 million years.
Its large family of moons gives rise to the most chaotic behaviour in the solar
system - that of Hyperion.
It has its own mini asteroid belt or ring system. The dynamics of ring systems
are incredibly complex and give rise to bands and gaps, very similar to the
asteroids. These depend on orbital resonances with the major moons and more
subtle interactions with shepherding moons (e.g. the F-ring). Its orbit is slowly
decreasing.
The 98° tilt of this gas giant points to a chaotic/catastrophic past - so too, the inner moon Miranda. Many orbits between Uranus and Neptune become chaotic and Uranus itself is seen to bounce around like a football between Saturn and Neptune over 100 million years or so.
Being the last major body in the solar system and the one that is furthest away from any perturbing influence, this gas giant exhibits only weak chaos in its orbit. It does have two fascinating moons that both have chaotic histories. The outermost moon, 170km long Nereid is an irregular chunk of ice and rock with a very dark surface that orbits in a highly inclined prograde orbit. Triton is bigger than Pluto and moves in an inclined retrograde orbit (unlike all the other major moons in the solar system). Its geologically young surface indicates much tidal heating and it is slowing down and spiralling into Neptune itself. It is thought to be a captured body.
This tiny double planet displays the most extreme irregularities in its motion. Not only does it possess the most inclined orbit in the solar system, but this orbit actually comes inside that of Neptune at present. The earliest integrations showed its 248 yr orbit oscillating in inclination through some 3° over a 38 million year period, together with a much longer cycle of 34 million years . The whole orbit was also shifting round with several cyclical variations of 37, 27 and 137 million years. Simulations indicated a lyapunov time of just 20 million yrs. Despite this the planet seemed well behaved because of a particular 3:2 orbital resonance with Neptune. This may have been instrumental in this planet's survival. Some scientists have theorised an early solar system filled with Pluto like objects in chaotic orbits, most of which were ejected or captured (like Triton). "Natural selection" favoured the particular orbital zone occupied by Pluto - although it may still be possible for this planet to tunnel into a violently chaotic zone and be ejected.
All these motions have been vividly captured on a video made by Jack Wisdom in 1992 that displays the evolution of the solar system at a rate of 60 000 yrs per second !
To summarize: to date the longest time span integration involving all nine
planets is 100 million yr - or 2% the age of the solar system. Calculations
based on secular theory now extend to 25 billion yrs into the future.
All the planets are still there, none has been ejected, fallen into the Sun
or collided with another planet and the overall configuration remains the same.
The behaviour of the planets is far from boring. Most show varying degrees of
chaotic behaviour and many show long term variations in orbital parameters that
are fairly regular, despite the chaos.
What implications does this have ?
In conclusion, The solar system is SIC - but it's not terminal!!