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

n 1605, Johannes Kepler discovered ing hand but is, in fact, naturally self- Ithat the orbits of the planets are el- correcting and stable. He calculated that lipses rather than combinations of cir- the gravitational interactions between cles, as astronomers had assumed since the planets would forever produce only antiquity. Isaac Newton was then able small oscillations of their orbital eccen- to prove that the same force of grav- tricities around their mean values. When ity that pulls apples to the ground also asked by his friend Napoleon why he keeps planets in their elliptical orbits did not mention God in his major work around the Sun. But Newton was wor- on celestial mechanics, Laplace is said to ried that the accumulated effects of the have replied, “Sir, I had no need for that weak gravitational tugs between neigh- hypothesis.” Laplace also thought that, boring planets would increase their or- given the exact position and momentum bital eccentricities (their deviations from of every object in the solar system at any circularity) until their paths eventually one time, it would be possible to calcu- crossed, leading to collisions and, ulti- late from the laws of motion precisely mately, to the destruction of the solar where everything would be at any fu- system. He believed that God must in- ture instant, no matter how remote. tervene, making planetary course cor- Laplace was correct to reject the need Figure 1. Some 4.6 billion years ago, before Earth existed, the Sun was surrounded by rections from time to time so as to keep for divine intervention to preserve the a disk of gas and dust, from which count- the heavens running smoothly. solar system, but not for the reasons he less small bodies were forming. Most of By 1800, the mathematician Pierre- thought. His calculations of stability these “planetesimals” coalesced into larger Simon Laplace had concluded that the were in fact incorrect. In the late 19th solar system requires no such guid- century, Henri Poincaré showed that La- discovering planetary systems around place had simplified some of his equa- many other stars. The evidence suggests tions by removing terms he wrongly as- that such systems may be filled nearly to Steven Soter received his doctorate in as- sumed to be superfluous, leading him to capacity. The abundance of observation- tronomy from Cornell University in 1971. He overlook the possibility of chaos in the al data from the newly found planetary is currently a research associate in the Depart- ment of Astrophysics at the American Museum solar system. Calculations with mod- systems will stimulate and test our ideas of Natural History in New York City and ern high-speed computers have finally about the delicate balance between order scientist-in-residence at New York University, provided evidence that the solar system and chaos among the worlds. where he teaches on subjects ranging from life is only marginally stable and that its de- in the universe to geology and antiquity in the tailed behavior is fundamentally unpre- Gaps in Understanding Mediterranean region. His research interests dictable over long time periods. In 1866, the American astronomer Dan- include planetary astronomy and geoarchae- Here I will outline some of the dis- iel Kirkwood produced the first real ev- ology. He collaborated with Carl Sagan and coveries that led to current ideas about idence for instability in the solar system Ann Druyan to create the acclaimed Cosmos instability in the evolution of the solar in his studies of the asteroid belt, which television series, which first aired on public system. Now is an especially promising lies between the orbits of Mars and Ju- television in 1980. This article is published in cooperation with NASA’s online Astrobiol- time to consider the subject. Theorists are piter. At the time, only about 90 aster- ogy Magazine (www.astrobio.net). Address: using powerful computer simulations oids were known (the orbits of more Hayden Planetarium, Central Park West at to explore the formation of planetary than 150,000 have since been charted), 79th Street, New York, NY 10024. Internet: systems under a wide range of starting but that meager population was suf- [email protected] conditions, while observers are rapidly ficient for Kirkwood to notice several

© 2007 Sigma Xi, The Scientific Research Society. Reproduction 414 American Scientist, Volume 95 with permission only. Contact [email protected]. ­planetary embryos, which grew larger still to become the eight planets of the solar system. Why eight? There is nothing special about the 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 pres- ent 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 or- the asteroid belt correspond, for exam- of the solar system. Asteroids that had bital periods or, equivalently, in their ple, to places where the orbital period been orbiting stably in the main belt orbital sizes. (The orbital periods of of Jupiter would have a ratio of 5:2 or are sometimes nudged into one of the planets, asteroids and comets increase 7:3 to that of an asteroid. resonant Kirkwood gaps, from which with orbital size in a well-defined way.) A simple way to understand reso- Jupiter eventually ejects them. These Kirkwood found that no asteroid had a nance is to push someone on a swing. gaps are like holes through which the period near 3.9 years, which, he noted, If you do so at random moments, not asteroid population is slowly drain- is one-third that of Jupiter. much happens. But if you shove each ing away. Many of the meteorites that An asteroid that orbits the Sun ex- time the swing returns to you, it will go strike Earth are fragments that were actly three times while Jupiter goes higher and higher. You could also push ejected from the asteroid belt after around just once would make its clos- at the same point on the arc but less straying into one of the resonant gaps. est approaches to the giant planet at the frequently, say only once every two Something similar takes place in the same point in its own orbit and get a or three cycles. The swing would then outer solar system. Gravitational tugs similar gravitational kick from its mas- take longer to reach a given height, the from the giant planets gradually re- sive celestial neighbor each time. The resonance being weaker. move icy worlds from the Kuiper belt, repeated tugs Jupiter exerted would An asteroid in such a resonant orbit which lies beyond the orbit of Nep- tend to add up, or resonate, from one can have its eccentricity increased until tune. This process supplies the short- passage to the next. Hence astronomers the body either collides with the Sun or period comets, which enter the inner refer to such an asteroid as being in a a planet, or encounters a planet closely solar system for a brief time and re- 3:1 mean-motion resonance. Other gaps in enough to be tossed into another part turn to it at regular intervals. In the

© 2007 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org 2007 September–October 415 with permission only. Contact [email protected]. +VQJUFSQFSJPE
SBUJP        fraction that managed to survive. The same is true of the asteroid belt. Gravi-  tational sculpting by the planets has severely depleted both populations, leaving the Kuiper and asteroid belts as remnants of the primordial plan- etesimal disk.  Whereas some mean-motion reso- nant orbits in the solar system are highly unstable, others are quite re- sistant to disruption. (The difference  depends on subtle details of the con- figuration of the interacting bodies.) 7FOVT +VQJUFS .FSDVSZ &BSUI .BST OVNCFS
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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 kilome- ters across are plotted here. A space-probe image of the near- Earth asteroid Eros (above) gives a sense of what most asteroids probably look like. Eros is about 30 kilometers long, much too +VQJUFS small for its gravity to make it spherical. (Diagram courtesy of the Minor Planet Center; image courtesy of NASA/Johns Hop- kins University Applied Physics Laboratory.)

© 2007 Sigma Xi, The Scientific Research Society. Reproduction 416 American Scientist, Volume 95 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 ellipti- cal 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 orbit- ing bodies are especially prone to disturbance. Figure 4. Numerical simulations conducted by Jacques Laskar revealed that the maximum Despite its orderly appearance, the orbital eccentricity of the inner planets changes considerably over time. Thus over billions of solar system actually includes many years, each planet would cut a broad swath (colored bands) around its mean orbit (white lines). elements of what mathematicians call 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 chaos. A defining feature of chaos is the way, they largely fill the inner solar system when one considers their long-term variations. extreme sensitivity of a system to its ini- (Adapted from Laskar 1996.) tial conditions. The most trivial distur- bance in such a system can profoundly computer power allowed mathemati- tions between all eight planets over a change its large-scale configuration at cians to explore it in sufficient detail. period of 25 billion years (five times the a later time. A pool table provides a fa- No one in Laplace’s day imagined that age of the solar system). Laskar found miliar example: Microscopic variations the solar system, then taken as the para- that the eccentricities and other ele- in the trajectory of a billiard ball, espe- digm of clockwork stability, is actually ments of the orbits undergo chaotic ex- cially one involved in multiple colli- vulnerable to chaos. cursions, which make it impossible to sions, can completely alter the outcome predict the locations of the planets after of the game. Chaotic systems are deter- Cleaning Up the Solar System a hundred million years. Does Laskar’s ministic, in that they follow precisely Jacques Laskar, of the Bureau des longi- result mean that the Earth might even- the laws of classical physics, but they tudes in Paris, has carried out the most tually find itself in a highly elliptical or- are fundamentally unpredictable. extensive calculations to investigate the bit, taking it much closer to and farther The nature of chaos was not well un- long-term stability of the solar system. from the Sun, or that the solar system derstood until recently, when increasing He simulated the gravitational interac- could lose a planet?

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Figure 5. Stable resonances are evident in the distribution of small bodies in the outer solar system (above). The Neptune Trojans, /FQUVOF 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 Kuiper- 1MVUP belt 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 www.americanscientist.org 2007 September–October 417 with permission only. Contact [email protected].  TUBSU “full” or very nearly so. That is, if you  tried to squeeze another planet in be-  tween the existing ones, the resulting  gravitational disturbances would dy- FDDFOUSJDJUZ  namically excite the system, leading to  
NJMMJPO a collision or ejection before the system ZFBST could settle down again. Laskar surmised that the solar sys- tem, at each stage of its evolution, was always near the edge of instability, as it appears to be today. To maintain its 
NJMMJPO ZFBST marginal stability, the solar system has been eliminating objects on a timescale comparable with its age at every ep- och. It follows that the solar system bil- lions of years ago may have contained 
NJMMJPO ZFBST more planets that it does now. UJNF According to this view, as the solar system matured, it managed to remain stable against the breakout of large- scale chaos by reducing the number 
NJMMJPO of planets and increasing the spacing ZFBST between them. The present number must be about as large (and their spac- ing about as small) as allowed by the system’s long-term stability. The solar


NJMMJPO system has increased its internal order ZFBST by exporting disorder—entropy—to the rest of the Galaxy, which receives the chaotically ejected objects. This process, called dynamical re- laxation, operates in star clusters and      in entire galaxies as well as in evolving PSCJUBM
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VOJUT planetary systems. As such systems expel their most unstable members, Figure 6. Numerical simulation reveals how the inner part of a planet-forming disk the orbits of the remaining objects be- evolves. Initially, such a disk is composed of numerous planetesimals in near-circular (low- come more compact. eccentricity) 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 Extensive computer simulations time goes on, the smaller bodies are swept up or scattered away, leaving a few planets in low- show that the eight planets greatly eccentricity orbits (bottom). Eccentricity ranges from 0 for circular orbits to 1 for unbound disturb the motions of test particles parabolas. (Adapted from Chambers 2001.) placed on circular orbits at most loca- tions in the solar system. Such particles No. Even chaos has to operate within which limits the excursions of orbital ec- are sent into close encounters with the physical limits. For example, although centricity for bodies of planetary mass. planets, which remove them in only a meteorologists cannot predict the The orbits of the giant outer planets few million years, a small fraction of weather (another chaotic system) as are the most stable. The smaller ter- the age of the solar system. But these far as a month in advance, they can be restrial planets, particularly Mars and simulations also identify several re- quite confident that conditions will fall Mercury, are more vigorously tossed gions where objects can survive for within a certain range, because external about. The simulations show that over far longer times. One such region is constraints (such as the Sun’s brightness millions of years the terrestrial planets a broad zone centered about half- and the length of the day) set limits on undergo substantial excursions in their way between the orbits of Mars and the overall system. eccentricities—large enough for those Jupiter—the asteroid belt. Computer Laskar found that, despite the influ- planets to clear out any debris from the simulations by Jack Lissauer and col- ence of chaos on the exact locations of intervening orbital space, but not large leagues at NASA Ames Research Cen- the planets, their orbits remain relative- enough to allow collisions between ter and at Queen’s University, Ontario, ly stable for billions of years. That is, them. However, Laskar found one pos- showed that if an Earth-sized planet whereas the long-term configuration is sible exception: Mercury, the lightest had formed there, it could remain in absolutely unpredictable in detail, the planet, has a small but finite chance of a stable orbit for billions of years. This orbits remain sufficiently well behaved colliding with Venus on a timescale of result is not too surprising, because to prevent collisions between neighbor- billions of years. He concluded that the the zone of the asteroid belt is well ing planets. An external constraint in solar system is “marginally stable.” populated and must therefore be rel- this case is imposed by the conservation Such results suggested to Laskar atively immune to disturbance. The of angular momentum in the system, that the solar system is dynamically same study found, however, that a gi-

© 2007 Sigma Xi, The Scientific Research Society. Reproduction 418 American Scientist, Volume 95 with permission only. Contact [email protected]. ant planet in the asteroid belt would mation, originally proposed by the well behaved. The embryos grow by soon become unstable. philosopher Immanuel Kant in 1755. capturing material from so-called feed- The Kuiper belt is another region of According to his nebular accretion the- ing zones in the disk, and their orbits stability, as there are no other planets ory, the solar system and other plan- become rather evenly spaced. But once to stir up the neighborhood beyond etary systems formed by the conden- the embryos have swept up most of the the orbit of Neptune. The Trojan as- sation and accumulation of dust and mass from the disk, the damping effect teroids of Mars, Jupiter and Neptune gas in flattened disks of debris orbit- becomes too feeble to keep the system occupy other protected interplanetary ing around young stars. The theory under control. The gravitational tugs niches. has found strong support in modern that the embryos exert on one another Aside from such islands of stabil- observations: Astronomers today rou- can then pump up their orbital eccen- ity, interplanetary space is remark- tinely detect such debris disks around tricities without limit. At that point, ably empty. Most of the small objects newborn stars. to use the vernacular, all hell breaks orbiting between the planets (such as The dust-sized particles in such a loose. In this final stage of planet for- Earth-crossing asteroids and short- disk first coagulate to form trillions mation, the orbits of the planetary em- period comets) are transient interlop- of rocky asteroids and icy comets a bryos begin to intersect, and the whole ers, which recently leaked into the few kilometers in diameter, called plan- system erupts into large-scale anarchy. neighborhood from the asteroid and etesimals. These objects in turn gently Entire worlds collide and merge, while Kuiper belts. The planets will soon collide and grow to produce scores to others are flung capriciously out into eject them or sweep them up in colli- hundreds of Moon- to Mars-sized bod- the Galaxy. sions. Indeed, a planet is now defined ies called planetary embryos, orbiting The observational evidence makes by the requirement that the object amid the swarm of remaining plan- it clear that the worlds formed in the has cleared its orbital neighborhood etesimals. Some embryos in the outer young solar system were subjected to of other material. Were it not for the parts of the disk grow large enough for intense bombardment, their surfaces leaky reservoirs that supply a steady their gravity to capture the abundant being saturated with craters. Many of trickle of debris to their vicinity, gas from the nebula, giving rise to gi- them are still covered with enormous the planets would have thoroughly ant planets. impact scars. Some moons and aster- cleaned out most of the orbital space As long as the planetesimals retain oids look like they were entirely blown between them. most of the mass in the disk, their apart and reassembled from frag- gravity locally exerts a damping effect ments. A Mars-sized planetary embryo Making Worlds Is a Messy Business (called dynamical friction) on the motion evidently collided with and entirely These ideas fit naturally into the pre- of the larger embedded embryos, and melted the proto-Earth, explosively vailing theory of solar system for- the whole system remains dynamically throwing off a great splash of debris,

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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.)

© 2007 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org 2007 September–October 419 with permission only. Contact [email protected]. ejections reduce the number of grow- PSCJU
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E ing planets and increase the average spacing between them. The planets D effectively compete for space, “el- bowing” each other apart. These numerical experiments con- firm that the formation of planets is C exquisitely sensitive to initial condi- F tions. For example, the displacement of only one in a hundred starting em- bryos along its orbit by only one me- ter, 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 exis- tence of Earth. Astronomers are now getting the chance to check whether such simula- tions reflect reality. For more than a decade, observers have been discover- ing and charting the configuration of other planetary systems, which were long assumed to exist. Planet hunt- ers 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 un- doubtedly exist around many of those F C D E stars, but current measurements can- not yet reveal them.     Astronomers were surprised to TFNJNBKPS
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"6 learn that most of the known extra- solar planets have orbits much more Figure 8. Studies of extrasolar systems offer astronomers increasing opportunity to test their eccentric than those of the giant plan- ideas about planet formation. The three innermost planets of star 55 Cancri, for example, ets in our solar system. It was gener- have 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 a suitable planet to support liquid water. The number above each planet in the bottom panel in nearly circular orbits. Perhaps, some shows its minimum mass, expressed in Earth masses. argued, our solar system is exception- 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, re- Mario Juric´ 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 under- to 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 ex- nearby 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 sur- now populate the distant Oort cloud, In such simulations, collisions and viving giant planets have lower orbital

© 2007 Sigma Xi, The Scientific Research Society. Reproduction 420 American Scientist, Volume 95 with permission only. Contact [email protected]. eccentricities, more like our own solar Barnes, now at the University of Barnes, R., and T. Quinn. 2004. The (in)stability system. Most of the simulations end Arizona, and Sean N. Raymond, at of planetary systems. The Astrophysical Jour- nal 611:494–516. up with two or three giant planets, af- the University of Colorado, went on Barnes, R., and S. N. Raymond. 2004. Predict- ter the ejection of at least half of the to hypothesize that all planetary sys- ing planets in known extrasolar planetary initial population. This result suggests tems are packed as tightly as possi- systems. I. Test particle simulations. The that free-floating planets, unattached ble, as Laskar had suggested earlier. Astrophysical Journal 617:569–574. to any star, are very common in the In some of the observed extrasolar Chambers, J. E. 2001. Making more terrestrial Galaxy. systems, Barnes and Raymond iden- planets. Icarus 152:205–224. Chambers, J. E. 2004. Planetary accretion in Other studies confirm that many of tified apparently empty regions of the inner solar system. Earth and Planetary the worlds initially populating a plan- stability around the central star. Science Letters 223:241–252. et-forming disk, if not most of them, Those regions, they predict, contain Juric´, M., and S. Tremaine. Submitted. Dynam- end up being tossed out into interstel- planets small enough to have evaded ical origin of extrasolar planet eccentricity lar space. The largest worlds left be- detection. distribution. The Astrophysical Journal. hind continue to grow by sweeping For example, the star 55 Cancri has Laskar, J. 1996. Large scale chaos and mar- ginal stability in the solar system. Celestial up smaller objects that remain bound four known giant planets, three of Mechanics and Dynamical Astronomy 64:115– to the central star. Making planets them close in with short orbital peri- 162. thus seems to be an extremely messy ods and a more distant planet with a Lecar, M, F. A. Franklin, M. Holman and N. business. A growing planetary system period of nearly 15 years. Between the W. Murray. 2001. Chaos in the solar system. resembles an overly energetic infant inner three and the outermost planet Annual Review of Astronomy and Astrophysics 39:581–631. learning to eat cereal with a spoon: lies a large area in which, Barnes and Levison, H. F., J. J. Lissauer and M. J. Dun- Some is consumed, but much of it ends Raymond predict, one or more new can. 1998. Modeling the diversity of outer up on the floor, walls and ceiling. planets will eventually be found. This planetary systems. The Astronomical Journal Most of the known extrasolar plan- region includes the “habitable zone,” 116:1998–2014. ets are more massive and have shorter where a planet’s surface temperature Lissauer, J. J. 1999. Chaotic motion in the solar system. Reviews of Modern Physics 71:835– periods and more eccentric orbits than would allow liquid water to exist. 845. the planets of our solar system. How- What we have here is a fascinating Lissauer, J. J., E. V. Quintana, E. J. Rivera and ever, that does not necessarily mean new hypothesis, which posits that our M. J. Duncan. 2001. The effect of a planet in that our system is anomalous. Current solar system and other mature plan- the asteroid belt on the orbital stability of observational techniques strongly fa- etary systems are filled nearly to ca- the terrestrial planets. Icarus 154:449–458. vor the discovery of massive planets pacity. The present configurations of Morbidelli, A. 2002. Modern integrations of so- lar system dynamics. Annual Review of Earth with orbital periods of only a few years such systems contain about as many and Planetary Sciences 30:89–112. or less, and even the giant planets of planets as they can hold, spaced about Murray, N., and M. Holman. 2001. The role our solar system, with their longer or- as closely together as stability allows. of chaotic resonances in the solar system. bital periods, would be near the limits Such is the expected outcome of the Nature 410:773–779. of detection if observed from the dis- chaotic process that makes planets. A O’Brien, D. P., A. Morbidelli and H. F. Levi- tance of a nearby star. family of planetary embryos grows by son. 2006. Terrestrial planet formation with strong dynamical friction. Icarus 184:39–58. feeding on a vast swarm of smaller Quintana, E. V., F. C. Adams, J. J. Lissauer and Worlds on the Edge objects in a debris disk until the system J. E. Chambers. 2007. Terrestrial planet for- A few years ago, Rory Barnes and loses its brakes. Global instability then mation around individual stars within bi- Thomas Quinn at the University of erupts, and the larger worlds consume nary star systems. The Astrophysical Journal Washington used computer simula- or eject the more erratic ones until the 660:807–822. Raymond, S. N., and R. Barnes. 2005. Predict- tions to examine the stability of extra­ system settles down into the mature ing planets in known extrasolar planetary solar systems having two or more state of marginal stability. The process systems. II. Testing for Saturn mass planets. planets. They found that almost all is one of self-organization, increasing The Astrophysical Journal 619:549–557. systems with planets that are close order within the system by exporting Raymond, S. N., R. Barnes, and N. A. Kaib. enough to affect one another gravita- disorder to the external environment, 2006. Predicting planets in known extra- tionally lie near the edge of instabil- in this case the Galaxy. solar planetary systems. III. Forming ter- restrial planets. The Astrophysical Journal ity. The simulations showed that small Like any good scientific hypothesis, 644:1223–1231. alterations in the orbits of the planets this one makes testable predictions. As- Raymond, S. N., T. Quinn and J. I. Lunine. in those systems would lead to cata- tronomers will search for new planets 2006. High-resolution simulations of the strophic disruptions. in the stable regions in other systems. final assembly of Earth-like planets. I. Ter- This remarkable result might This process may take a long time, be- restrial accretion and dynamics. Icarus 183:265–282. seem surprising. But the prevalence cause the smaller planets are very dif- Soter, S. 2006. What is a planet? The Astronomi- of such marginally stable systems ficult to detect, but as observational cal Journal 132:2513–2519. makes sense, Barnes and Quinn con- methods continue to improve, we will cluded, if planets form within unsta- eventually find out whether the idea of ble systems that become more stable “packed planetary systems” stands up by ejecting massive bodies. The in- to critical scrutiny. For relevant Web links, consult this ­issue of American Scientist Online: vestigators remarked, “As unsettling as it may be, it seems that a large Bibliography http://www.americanscientist.org/ Issue TOC/issue/1001 fraction of planetary systems, includ- Adams, F. C., and G. Laughlin. 2003. Migration ing our own, lie dangerously close to and dynamical relaxation in crowded sys- instability.” tems of giant planets. Icarus 163:290–306.

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