Download American Scientist - Lunar and Planetary Laboratory

A reprint from
American Scientist
the magazine of Sigma Xi, The Scientific Research Society
This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions,
American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected].
©Sigma Xi, The Scientific Research Society and other rightsholders
Are Planetary Systems
Filled to Capacity?
Computer simulations suggest that the answer may
be yes. But observations of extrasolar systems will
provide the ultimate test
Steven Soter
I
n 1605, Johannes Kepler discovered
that the orbits of the planets are ellipses rather than combinations of circles, as astronomers had assumed since
antiquity. Isaac Newton was then able
to prove that the same force of gravity that pulls apples to the ground also
keeps planets in their elliptical orbits
around the Sun. But Newton was worried that the accumulated effects of the
weak gravitational tugs between neighboring planets would increase their orbital eccentricities (their deviations from
circularity) until their paths eventually
crossed, leading to collisions and, ultimately, to the destruction of the solar
system. He believed that God must intervene, making planetary course corrections from time to time so as to keep
the heavens running smoothly.
By 1800, the mathematician PierreSimon Laplace had concluded that the
solar system requires no such guidSteven Soter received his doctorate in astronomy from Cornell University in 1971. He
is currently a research associate in the Department of Astrophysics at the American Museum
of Natural History in New York City and
scientist-in-residence at New York University,
where he teaches on subjects ranging from life
in the universe to geology and antiquity in the
Mediterranean region. His research interests
include planetary astronomy and geoarchaeology. He collaborated with Carl Sagan and
Ann Druyan to create the acclaimed Cosmos
television series, which first aired on public
television in 1980. This article is published in
cooperation with NASA’s online Astrobiology Magazine (www.astrobio.net). Address:
Hayden Planetarium, Central Park West at
79th Street, New York, NY 10024. Internet:
[email protected]
414
American Scientist, Volume 95
ing hand but is, in fact, naturally selfcorrecting and stable. He calculated that
the gravitational interactions between
the planets would forever produce only
small oscillations of their orbital eccentricities around their mean values. When
asked by his friend Napoleon why he
did not mention God in his major work
on celestial mechanics, Laplace is said to
have replied, “Sir, I had no need for that
hypothesis.” Laplace also thought that,
given the exact position and momentum
of every object in the solar system at any
one time, it would be possible to calculate from the laws of motion precisely
where everything would be at any future instant, no matter how remote.
Laplace was correct to reject the need
for divine intervention to preserve the
solar system, but not for the reasons he
thought. His calculations of stability
were in fact incorrect. In the late 19th
century, Henri Poincaré showed that Laplace had simplified some of his equations by removing terms he wrongly assumed to be superfluous, leading him to
overlook the possibility of chaos in the
solar system. Calculations with modern high-speed computers have finally
provided evidence that the solar system
is only marginally stable and that its detailed behavior is fundamentally unpredictable over long time periods.
Here I will outline some of the discoveries that led to current ideas about
instability in the evolution of the solar
system. Now is an especially promising
time to consider the subject. Theorists are
using powerful computer simulations
to explore the formation of planetary
systems under a wide range of starting
conditions, while observers are rapidly
Figure 1. Some 4.6 billion years ago, before
Earth existed, the Sun was surrounded by
a disk of gas and dust, from which countless small bodies were forming. Most of
these “planetesimals” coalesced into larger
discovering planetary systems around
many other stars. The evidence suggests
that such systems may be filled nearly to
capacity. The abundance of observational data from the newly found planetary
systems will stimulate and test our ideas
about the delicate balance between order
and chaos among the worlds.
Gaps in Understanding
In 1866, the American astronomer Daniel Kirkwood produced the first real evidence for instability in the solar system
in his studies of the asteroid belt, which
lies between the orbits of Mars and Jupiter. At the time, only about 90 asteroids were known (the orbits of more
than 150,000 have since been charted),
but that meager population was sufficient for Kirkwood to notice several
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
­ lanetary embryos, which grew larger still to become the eight planets of the solar system. Why eight? There is nothing special about the
p
number. Chaotic encounters between planetesimals early on led to a system with enough large bodies to sweep up most of the smaller ones.
Computer simulations suggest that such encounters could as readily have ended up with fewer or more planets—but not too many. The present configuration of the solar system is filled nearly to capacity, and additional planets would be dynamically unstable. (Artist’s rendering of
a hypothetical planetary system in the making, by Tim Pyle, courtesy of NASA/JPL-Caltech.)
“gaps” in the distribution of their orbital periods or, equivalently, in their
orbital sizes. (The orbital periods of
planets, asteroids and comets increase
with orbital size in a well-defined way.)
Kirkwood found that no asteroid had a
period near 3.9 years, which, he noted,
is one-third that of Jupiter.
An asteroid that orbits the Sun exactly three times while Jupiter goes
around just once would make its closest approaches to the giant planet at the
same point in its own orbit and get a
similar gravitational kick from its massive celestial neighbor each time. The
repeated tugs Jupiter exerted would
tend to add up, or resonate, from one
passage to the next. Hence astronomers
refer to such an asteroid as being in a
3:1 mean-motion resonance. Other gaps in
www.americanscientist.org
the asteroid belt correspond, for example, to places where the orbital period
of Jupiter would have a ratio of 5:2 or
7:3 to that of an asteroid.
A simple way to understand resonance is to push someone on a swing.
If you do so at random moments, not
much happens. But if you shove each
time the swing returns to you, it will go
higher and higher. You could also push
at the same point on the arc but less
frequently, say only once every two
or three cycles. The swing would then
take longer to reach a given height, the
resonance being weaker.
An asteroid in such a resonant orbit
can have its eccentricity increased until
the body either collides with the Sun or
a planet, or encounters a planet closely
enough to be tossed into another part
of the solar system. Asteroids that had
been orbiting stably in the main belt
are sometimes nudged into one of the
resonant Kirkwood gaps, from which
Jupiter eventually ejects them. These
gaps are like holes through which the
asteroid population is slowly draining away. Many of the meteorites that
strike Earth are fragments that were
ejected from the asteroid belt after
straying into one of the resonant gaps.
Something similar takes place in the
outer solar system. Gravitational tugs
from the giant planets gradually remove icy worlds from the Kuiper belt,
which lies beyond the orbit of Neptune. This process supplies the shortperiod comets, which enter the inner
solar system for a brief time and return to it at regular intervals. In the
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
2007 September–October
415
+VQJUFSQFSJPESBUJP
+VQJUFS
.BST
7FOVT
&BSUI
.FSDVSZ
OVNCFSPGPCKFDUTUIPVTBOET
PSCJUBMTFNJNBKPSBYJTBTUSPOPNJDBMVOJUT
Figure 2. Resonant effects can be clearly seen in the radial distribution of the asteroids. Some
orbital resonances are destabilizing, creating minima in the distribution, called “Kirkwood
gaps” after Daniel Kirkwood, the astronomer who first recognized them. The main asteroid belt
is bounded by the 4:1 and 2:1 orbital resonances with Jupiter. The stable 3:2 and 1:1 resonances
account, respectively, for the Hilda family of asteroids and the Jupiter Trojans. The semimajor
axis is one-half the long dimension of an object’s elliptical orbit. One astronomical unit is the
Earth-Sun distance. (Distribution of asteroids courtesy of the Minor Planet Center.)
early solar system, close encounters
of small icy bodies with the growing
giant planets populated the distant
Oort cloud with hundreds of billions
of cometary nuclei.
Such interactions also caused the orbits of the major planets to migrate.
Because the growing planets Saturn,
Uranus and Neptune tossed more
small bodies inward toward the orbit
of Jupiter than out of the solar system,
those planets migrated outward, to
conserve the total angular momentum.
But the much more massive planet Jupiter ejected most of the small bodies
it encountered into the outer solar system and beyond, and it consequently
migrated inward. When the solar system was forming, the Kuiper belt contained hundreds of times more mass
than it does today. The objects now
in the belt represent only the small
Figure 3. The main asteroid belt, situated in the broad region
betweeen the orbits of Mars and Jupiter, contains countless
rocky bodies (white points in diagram). The Trojan asteroids
(pink) can survive outside this belt because they are locked in
a 1:1 orbital resonance with Jupiter, which keeps them spaced
safely about 60 degrees ahead of or behind that giant planet in
its orbit. For clarity, only asteroids larger than about 50 kilometers across are plotted here. A space-probe image of the nearEarth asteroid Eros (above) gives a sense of what most asteroids
probably look like. Eros is about 30 kilometers long, much too
small for its gravity to make it spherical. (Diagram courtesy of
the Minor Planet Center; image courtesy of NASA/Johns Hopkins University Applied Physics Laboratory.)
416
American Scientist, Volume 95
fraction that managed to survive. The
same is true of the asteroid belt. Gravitational sculpting by the planets has
severely depleted both populations,
leaving the Kuiper and asteroid belts
as remnants of the primordial planetesimal disk.
Whereas some mean-motion resonant orbits in the solar system are
highly unstable, others are quite resistant to disruption. (The difference
depends on subtle details of the configuration of the interacting bodies.)
Many of the objects in the Kuiper
belt have their orbits locked in a stable 2:3 mean-motion resonance with
Neptune. They orbit the Sun twice
for every three orbits of this planet.
Such objects are called plutinos, after
Pluto, the first one discovered. Some
of them, including Pluto, cross inside
the orbit of Neptune, but the geometry of their resonant orbits keeps
them from making close approaches
to the planet and accounts for their
survival.
Thousands of small worlds called
Trojan asteroids share Jupiter’s orbit
around the Sun, leading or following
the planet by about 60 degrees. These
bodies are trapped in a so-called 1:1
mean-motion resonance, the planet
and asteroid having the same orbital
period. This configuration inhibits
close approaches to Jupiter and is relatively stable. Similar families of coorbital asteroids accompany both
Neptune and Mars around the Sun.
+VQJUFS
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
Gravitational tugs of the planets on
one another produce cyclical motions
in the spatial orientation of their orbits,
causing another kind of resonance. The
rotation of the orientation of an elliptical orbit takes many times longer than
the orbital period of the planet itself.
These slow gyrations of an entire orbit
produce so-called secular resonances,
which can strongly distort the orbits
of smaller bodies—and not just those
in the asteroid belt. The solar system
is crowded with potential orbits on
which objects would be subjected to
secular or mean-motion resonances.
Many resonant orbits overlap, and
wherever that happens, small orbiting bodies are especially prone to
disturbance.
Despite its orderly appearance, the
solar system actually includes many
elements of what mathematicians call
chaos. A defining feature of chaos is the
extreme sensitivity of a system to its initial conditions. The most trivial disturbance in such a system can profoundly
change its large-scale configuration at
a later time. A pool table provides a familiar example: Microscopic variations
in the trajectory of a billiard ball, especially one involved in multiple collisions, can completely alter the outcome
of the game. Chaotic systems are deterministic, in that they follow precisely
the laws of classical physics, but they
are fundamentally unpredictable.
The nature of chaos was not well understood until recently, when increasing
Figure 4. Numerical simulations conducted by Jacques Laskar revealed that the maximum
orbital eccentricity of the inner planets changes considerably over time. Thus over billions of
years, each planet would cut a broad swath (colored bands) around its mean orbit (white lines).
Indeed, Mercury’s orbital eccentricity can, in principle, become large enough that it risks
collision with Venus. Although the orbits of other terrestrial planets will never cross in this
way, they largely fill the inner solar system when one considers their long-term variations.
(Adapted from Laskar 1996.)
computer power allowed mathematicians to explore it in sufficient detail.
No one in Laplace’s day imagined that
the solar system, then taken as the paradigm of clockwork stability, is actually
vulnerable to chaos.
Cleaning Up the Solar System
Jacques Laskar, of the Bureau des longitudes in Paris, has carried out the most
extensive calculations to investigate the
long-term stability of the solar system.
He simulated the gravitational interac
tions between all eight planets over a
period of 25 billion years (five times the
age of the solar system). Laskar found
that the eccentricities and other elements of the orbits undergo chaotic excursions, which make it impossible to
predict the locations of the planets after
a hundred million years. Does Laskar’s
result mean that the Earth might eventually find itself in a highly elliptical orbit, taking it much closer to and farther
from the Sun, or that the solar system
could lose a planet?
/FQUVOFQFSJPESBUJP
FDDFOUSJDJUZ
1MVUP
PSCJUBMTFNJNBKPSBYJTBTUSPOPNJDBMVOJUT
/FQUVOF
1MVUP
www.americanscientist.org
Figure 5. Stable resonances are evident in the distribution of small
bodies in the outer solar system (above). The Neptune Trojans,
objects in a 1:1 resonance with that planet, orbit at 30 astronomical
units from the Sun. Reaching farther out are the orbits of the Kuiperbelt objects, including Pluto and its fellow “plutinos” (which share
a stabilizing 2:3 resonance with Neptune) and objects locked into 3:4
and 1:2 resonances. Most of the plutinos (left, pink points) and other
Kuiper-belt objects (white) are located outside the orbit of Neptune.
For clarity, transient comets and scattered Kuiper-belt objects are not
shown. (Plan view courtesy of the Minor Planet Center.)
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
2007 September–October
417
FD
DF
O
USJ
DJ
UZ
TUBSU
NJMMJPO
ZFBST
NJMMJPO
ZFBST
UJNF
NJMMJPO
ZFBST
NJMMJPO
ZFBST
NJMMJPO
ZFBST
PSCJUBMTFNJNBKPSBYJTBTUSPOPNJDBMVOJUT
Figure 6. Numerical simulation reveals how the inner part of a planet-forming disk
evolves. Initially, such a disk is composed of numerous planetesimals in near-circular (loweccentricity) orbits (top). Within a few million years, orbital eccentricities grow to appreciable
size for most of the smaller bodies, and planetary embryos form as smaller objects coalesce. As
time goes on, the smaller bodies are swept up or scattered away, leaving a few planets in loweccentricity orbits (bottom). Eccentricity ranges from 0 for circular orbits to 1 for unbound
parabolas. (Adapted from Chambers 2001.)
No. Even chaos has to operate within
physical limits. For example, although
meteorologists cannot predict the
weather (another chaotic system) as
far as a month in advance, they can be
quite confident that conditions will fall
within a certain range, because external
constraints (such as the Sun’s brightness
and the length of the day) set limits on
the overall system.
Laskar found that, despite the influence of chaos on the exact locations of
the planets, their orbits remain relatively stable for billions of years. That is,
whereas the long-term configuration is
absolutely unpredictable in detail, the
orbits remain sufficiently well behaved
to prevent collisions between neighboring planets. An external constraint in
this case is imposed by the conservation
of angular momentum in the system,
418
American Scientist, Volume 95
which limits the excursions of orbital eccentricity for bodies of planetary mass.
The orbits of the giant outer planets
are the most stable. The smaller terrestrial planets, particularly Mars and
Mercury, are more vigorously tossed
about. The simulations show that over
millions of years the terrestrial planets
undergo substantial excursions in their
eccentricities—large enough for those
planets to clear out any debris from the
intervening orbital space, but not large
enough to allow collisions between
them. However, Laskar found one possible exception: Mercury, the lightest
planet, has a small but finite chance of
colliding with Venus on a timescale of
billions of years. He concluded that the
solar system is “marginally stable.”
Such results suggested to Laskar
that the solar system is dynamically
“full” or very nearly so. That is, if you
tried to squeeze another planet in between the existing ones, the resulting
gravitational disturbances would dynamically excite the system, leading to
a collision or ejection before the system
could settle down again.
Laskar surmised that the solar system, at each stage of its evolution, was
always near the edge of instability, as
it appears to be today. To maintain its
marginal stability, the solar system has
been eliminating objects on a timescale
comparable with its age at every epoch. It follows that the solar system billions of years ago may have contained
more planets that it does now.
According to this view, as the solar
system matured, it managed to remain
stable against the breakout of largescale chaos by reducing the number
of planets and increasing the spacing
between them. The present number
must be about as large (and their spacing about as small) as allowed by the
system’s long-term stability. The solar
system has increased its internal order
by exporting disorder—entropy—to
the rest of the Galaxy, which receives
the chaotically ejected objects.
This process, called dynamical relaxation, operates in star clusters and
in entire galaxies as well as in evolving
planetary systems. As such systems
expel their most unstable members,
the orbits of the remaining objects become more compact.
Extensive computer simulations
show that the eight planets greatly
disturb the motions of test particles
placed on circular orbits at most locations in the solar system. Such particles
are sent into close encounters with the
planets, which remove them in only a
few million years, a small fraction of
the age of the solar system. But these
simulations also identify several regions where objects can survive for
far longer times. One such region is
a broad zone centered about halfway between the orbits of Mars and
Jupiter—the asteroid belt. Computer
simulations by Jack Lissauer and colleagues at NASA Ames Research Center and at Queen’s University, Ontario,
showed that if an Earth-sized planet
had formed there, it could remain in
a stable orbit for billions of years. This
result is not too surprising, because
the zone of the asteroid belt is well
populated and must therefore be relatively immune to disturbance. The
same study found, however, that a gi-
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
ant planet in the asteroid belt would
soon become unstable.
The Kuiper belt is another region of
stability, as there are no other planets
to stir up the neighborhood beyond
the orbit of Neptune. The Trojan asteroids of Mars, Jupiter and Neptune
occupy other protected interplanetary
niches.
Aside from such islands of stability, interplanetary space is remarkably empty. Most of the small objects
orbiting between the planets (such as
Earth-crossing asteroids and shortperiod comets) are transient interlopers, which recently leaked into the
neighborhood from the asteroid and
Kuiper belts. The planets will soon
eject them or sweep them up in collisions. Indeed, a planet is now defined
by the requirement that the object
has cleared its orbital neighborhood
of other material. Were it not for the
leaky reservoirs that supply a steady
trickle of debris to their vicinity,
the planets would have thoroughly
cleaned out most of the orbital space
between them.
Making Worlds Is a Messy Business
These ideas fit naturally into the prevailing theory of solar system for
B
mation, originally proposed by the
philosopher Immanuel Kant in 1755.
According to his nebular accretion theory, the solar system and other planetary systems formed by the condensation and accumulation of dust and
gas in flattened disks of debris orbiting around young stars. The theory
has found strong support in modern
observations: Astronomers today routinely detect such debris disks around
newborn stars.
The dust-sized particles in such a
disk first coagulate to form trillions
of rocky asteroids and icy comets a
few kilometers in diameter, called planetesimals. These objects in turn gently
collide and grow to produce scores to
hundreds of Moon- to Mars-sized bodies called planetary embryos, orbiting
amid the swarm of remaining planetesimals. Some embryos in the outer
parts of the disk grow large enough for
their gravity to capture the abundant
gas from the nebula, giving rise to giant planets.
As long as the planetesimals retain
most of the mass in the disk, their
gravity locally exerts a damping effect
(called dynamical friction) on the motion
of the larger embedded embryos, and
the whole system remains dynamically
/FQUVOF
H
4BUVSO 6SBOVT
C
I
D
J
E
K
L
F
M
G
+VQJUFS
well behaved. The embryos grow by
capturing material from so-called feeding zones in the disk, and their orbits
become rather evenly spaced. But once
the embryos have swept up most of the
mass from the disk, the damping effect
becomes too feeble to keep the system
under control. The gravitational tugs
that the embryos exert on one another
can then pump up their orbital eccentricities without limit. At that point,
to use the vernacular, all hell breaks
loose. In this final stage of planet formation, the orbits of the planetary embryos begin to intersect, and the whole
system erupts into large-scale anarchy.
Entire worlds collide and merge, while
others are flung capriciously out into
the Galaxy.
The observational evidence makes
it clear that the worlds formed in the
young solar system were subjected to
intense bombardment, their surfaces
being saturated with craters. Many of
them are still covered with enormous
impact scars. Some moons and asteroids look like they were entirely blown
apart and reassembled from fragments. A Mars-sized planetary embryo
evidently collided with and entirely
melted the proto-Earth, explosively
throwing off a great splash of debris,
PSCJUBMTFNJNBKPSBYJTJOBTUSPOPNJDBMVOJUT"6
PSCJUBMTFNJNBKPSBYJTJOBTUSPOPNJDBMVOJUT"6
Figure 7. Simulations suggest the wide variety of outer planetary systems that planetesimal disks can produce. The outer solar system is shown
for comparison (a). The simulated planetary systems that resulted from these 11 experimental runs range from having just one (b) to as many
as seven (f) outer planets of varying mass (indicated above each planet in Earth masses). The different outcomes depend on the initial number
and distribution of planetesimals and the chaotic interactions between them. (Adapted from Levison et al. 1998.)
www.americanscientist.org
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
2007 September–October
419
ejections reduce the number of growing planets and increase the average
spacing between them. The planets
D
effectively compete for space, “elbowing” each other apart.
These numerical experiments confirm that the formation of planets is
C
exquisitely sensitive to initial conditions. For example, the displacement
F
of only one in a hundred starting embryos along its orbit by only one meter, keeping everything else the same
in a simulation, can make the differ"6
ence between ending up with three
terrestrial planets or five. Such results
strongly suggest that a trivial chance
encounter determined the very existence of Earth.
Astronomers are now getting the
chance to check whether such simulations reflect reality. For more than a
decade, observers have been discovering and charting the configuration of
other planetary systems, which were
long assumed to exist. Planet hunters have already detected more than
240 worlds orbiting around other stars,
more than 60 of them in systems hav"6
ing two or more known planets. So far,
the observing techniques are limited to
detecting giant planets, in most cases
at least 10 times more massive than
Earth. Smaller terrestrial planets undoubtedly exist around many of those
F
C
D
E
stars, but current measurements cannot yet reveal them.
Astronomers were surprised to
TFNJNBKPSBYJTJOBTUSPOPNJDBMVOJUT"6
learn that most of the known extrasolar planets have orbits much more
Figure 8. Studies of extrasolar systems offer astronomers increasing opportunity to test their
eccentric than those of the giant planideas about planet formation. The three innermost planets of star 55 Cancri, for example,
ets in our solar system. It was generhave orbits smaller than that of Mercury. These three planets are separated from a much more
ally assumed that the other systems
massive world by a region of apparent stability, which is predicted to harbor another planet.
would resemble our own, with planets
This region encompasses the star’s habitable zone, where surface temperatures would allow
in nearly circular orbits. Perhaps, some
a suitable planet to support liquid water. The number above each planet in the bottom panel
argued, our solar system is exceptionshows its minimum mass, expressed in Earth masses.
al and most planetary systems were
some part of which reassembled to loosely bound by the Sun’s gravity. formed in a different way. This now
form the Moon.
Some of them, further nudged by looks unlikely.
As the growing planets swallowed passing stars and galactic tides, reMario Jurić and Scott Tremaine
up planetesimals from the debris enter the inner solar system as spec- at Princeton University recently ran
disk, they were also ejecting count- tacular long-period comets.
thousands of computer simulations to
less others to great distances. Many
Theorists today use computer follow the dynamical evolution of 10
of those objects had enough energy models to simulate the late stages of or more giant planets in a disk underto escape to interstellar space, where planetary formation. They can follow going collisions, mergers and ejections.
they now drift between the stars. the dynamical evolution of such sys- For simulations that begin with planets
Others, flung without quite enough tems, using a range of starting con- relatively close together, the ones that
velocity to escape, reached the out- ditions to represent different debris survive to the end have a distribution
ermost fringes of the solar system, disks. Some of the simulations gener- of orbital eccentricities that beautifully
where the gravitational influence of ate planets with orbits and masses matches the data for the observed exnearby stars and the Galaxy itself that resemble those in our solar sys- trasolar planets. For simulations that
could circularize their orbits. Hun- tem. Others produce systems with begin with the planets farther apart,
dreds of billions of these icy objects giant planets in more eccentric orbits. leading to fewer interactions, the surnow populate the distant Oort cloud, In such simulations, collisions and viving giant planets have lower orbital
PSCJUPGQMBOFUE
420
American Scientist, Volume 95
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
eccentricities, more like our own solar
system. Most of the simulations end
up with two or three giant planets, after the ejection of at least half of the
initial population. This result suggests
that free-floating planets, unattached
to any star, are very common in the
Galaxy.
Other studies confirm that many of
the worlds initially populating a planet-forming disk, if not most of them,
end up being tossed out into interstellar space. The largest worlds left behind continue to grow by sweeping
up smaller objects that remain bound
to the central star. Making planets
thus seems to be an extremely messy
business. A growing planetary system
resembles an overly energetic infant
learning to eat cereal with a spoon:
Some is consumed, but much of it ends
up on the floor, walls and ceiling.
Most of the known extrasolar planets are more massive and have shorter
periods and more eccentric orbits than
the planets of our solar system. However, that does not necessarily mean
that our system is anomalous. Current
observational techniques strongly favor the discovery of massive planets
with orbital periods of only a few years
or less, and even the giant planets of
our solar system, with their longer orbital periods, would be near the limits
of detection if observed from the distance of a nearby star.
Worlds on the Edge
A few years ago, Rory Barnes and
Thomas Quinn at the University of
Washington used computer simulations to examine the stability of extra­
solar systems having two or more
planets. They found that almost all
systems with planets that are close
enough to affect one another gravitationally lie near the edge of instability. The simulations showed that small
alterations in the orbits of the planets
in those systems would lead to catastrophic disruptions.
This remarkable result might
seem surprising. But the prevalence
of such marginally stable systems
makes sense, Barnes and Quinn concluded, if planets form within unstable systems that become more stable
by ejecting massive bodies. The investigators remarked, “As unsettling
as it may be, it seems that a large
fraction of planetary systems, including our own, lie dangerously close to
instability.”
www.americanscientist.org
Barnes, now at the University of
Arizona, and Sean N. Raymond, at
the University of Colorado, went on
to hypothesize that all planetary systems are packed as tightly as possible, as Laskar had suggested earlier.
In some of the observed extrasolar
systems, Barnes and Raymond identified apparently empty regions of
stability around the central star.
Those regions, they predict, contain
planets small enough to have evaded
detection.
For example, the star 55 Cancri has
four known giant planets, three of
them close in with short orbital periods and a more distant planet with a
period of nearly 15 years. Between the
inner three and the outermost planet
lies a large area in which, Barnes and
Raymond predict, one or more new
planets will eventually be found. This
region includes the “habitable zone,”
where a planet’s surface temperature
would allow liquid water to exist.
What we have here is a fascinating
new hypothesis, which posits that our
solar system and other mature planetary systems are filled nearly to capacity. The present configurations of
such systems contain about as many
planets as they can hold, spaced about
as closely together as stability allows.
Such is the expected outcome of the
chaotic process that makes planets. A
family of planetary embryos grows by
feeding on a vast swarm of smaller
objects in a debris disk until the system
loses its brakes. Global instability then
erupts, and the larger worlds consume
or eject the more erratic ones until the
system settles down into the mature
state of marginal stability. The process
is one of self-organization, increasing
order within the system by exporting
disorder to the external environment,
in this case the Galaxy.
Like any good scientific hypothesis,
this one makes testable predictions. Astronomers will search for new planets
in the stable regions in other systems.
This process may take a long time, because the smaller planets are very difficult to detect, but as observational
methods continue to improve, we will
eventually find out whether the idea of
“packed planetary systems” stands up
to critical scrutiny.
Barnes, R., and T. Quinn. 2004. The (in)stability
of planetary systems. The Astrophysical Journal 611:494–516.
Barnes, R., and S. N. Raymond. 2004. Predicting planets in known extrasolar planetary
systems. I. Test particle simulations. The
Astrophysical Journal 617:569–574.
Chambers, J. E. 2001. Making more terrestrial
planets. Icarus 152:205–224.
Chambers, J. E. 2004. Planetary accretion in
the inner solar system. Earth and Planetary
Science Letters 223:241–252.
Jurić, M., and S. Tremaine. Submitted. Dynamical origin of extrasolar planet eccentricity
distribution. The Astrophysical Journal.
Laskar, J. 1996. Large scale chaos and marginal stability in the solar system. Celestial
Mechanics and Dynamical Astronomy 64:115–
162.
Lecar, M, F. A. Franklin, M. Holman and N.
W. Murray. 2001. Chaos in the solar system.
Annual Review of Astronomy and Astrophysics
39:581–631.
Levison, H. F., J. J. Lissauer and M. J. Duncan. 1998. Modeling the diversity of outer
planetary systems. The Astronomical Journal
116:1998–2014.
Lissauer, J. J. 1999. Chaotic motion in the solar
system. Reviews of Modern Physics 71:835–
845.
Lissauer, J. J., E. V. Quintana, E. J. Rivera and
M. J. Duncan. 2001. The effect of a planet in
the asteroid belt on the orbital stability of
the terrestrial planets. Icarus 154:449–458.
Morbidelli, A. 2002. Modern integrations of solar system dynamics. Annual Review of Earth
and Planetary Sciences 30:89–112.
Murray, N., and M. Holman. 2001. The role
of chaotic resonances in the solar system.
Nature 410:773–779.
O’Brien, D. P., A. Morbidelli and H. F. Levison. 2006. Terrestrial planet formation with
strong dynamical friction. Icarus 184:39–58.
Quintana, E. V., F. C. Adams, J. J. Lissauer and
J. E. Chambers. 2007. Terrestrial planet formation around individual stars within binary star systems. The Astrophysical Journal
660:807–822.
Raymond, S. N., and R. Barnes. 2005. Predicting planets in known extrasolar planetary
systems. II. Testing for Saturn mass planets.
The Astrophysical Journal 619:549–557.
Raymond, S. N., R. Barnes, and N. A. Kaib.
2006. Predicting planets in known extrasolar planetary systems. III. Forming terrestrial planets. The Astrophysical Journal
644:1223–1231.
Raymond, S. N., T. Quinn and J. I. Lunine.
2006. High-resolution simulations of the
final assembly of Earth-like planets. I. Terrestrial accretion and dynamics. Icarus
183:265–282.
Soter, S. 2006. What is a planet? The Astronomical Journal 132:2513–2519.
Bibliography
Adams, F. C., and G. Laughlin. 2003. Migration
and dynamical relaxation in crowded systems of giant planets. Icarus 163:290–306.
© 2007 Sigma Xi, The Scientific Research Society. Reproduction
with permission only. Contact [email protected].
For relevant Web links, consult this
i­ssue of American Scientist Online:
http://www.americanscientist.org/
Issue TOC/issue/1001
2007 September–October
421