Migrating Planets Migrating Scientific American by Renumalhotra May Havecaused Theplanettomigrateitscurrent Orbit

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56 Migrating Planets Migrating Scientific American by RenuMalhotra may havecaused theplanettomigrateitscurrent orbit. gy, anditsorbitspiraledoutward veryslightly. Billionsofsuchencounters from thesolarsystem ( were scatteredbyNeptune’s gravitytoward Jupiter, whichejectedthem icy bodiescalledplanetesimals( NEWLY FORMEDNEPTUNEtraveled amidaswarmofsmallrockyand September 1999 above Did thesolarsystemalways look ). Inatypicalscattering, Neptunegainedener- opposite page ). Somehittheplanetbutmost the way itdoesnow? New evidence indicates thatthe outer planetsmayhave Copyright 1999Scientific American,Inc. migrated totheir NEPTUNE present orbits PLANETESIMAL

JANA BRENNING; DON DIXON (inset) I planets havemaintainedthis celestial mer r r for almostthe entir this ver motions, andmathematical models showthat the solarsystem. Itistempting,then,toassume espectful distancefr ound sinceastr in itsownwell-deﬁnedorbit, maintaining a system, eachplanetmovesar n thefamiliarvisualr y stableorbitalconﬁguration hasexisted onomers beganr e 4.5-billion-year histor om itsneighbors.The enditions ofthesolar Copyright 1999 Scientific American, Inc. ecor ound thesun ding their r y-go- y of we nowobser that theplanetswer distribution within thesolarnebula.W of theplanets have beenusedtoinferthemass gave risetothesolarsystem. Theorbitalradii nebula, theprimor the sunindicatetheirbir that theobser er n-day astr Cer tainly itisthesimplesthypothesis. Mod onomers havegenerallypr ve. ved distancesoftheplanetsfr dial diskofdustandgasthat e “bor thplaces inthesolar n” intheorbitsthat esumed ith this om -

DON DIXON PLUTO URANUS NEPTUNE JUPITER SATURN SUN

URANUS NEPTUNE SUN JUPITER SATURN PLUTO

basic information, theorists have derived comets and asteroids—undergo a more which in turn has a period twice that of constraints on the nature and timescales gradual orbital evolution, gently spiral- Io. This precise synchronization is be- of planetary formation. Consequently, ing in toward the sun and raining down lieved to be the result of a gradual evo- much of our understanding of the early on the planets in their path. lution of the satellites’ orbits by means history of the solar system is based on Furthermore, the orbits of many plan- of tidal forces exerted by the planet they the assumption that the planets formed etary satellites have changed significant- are circling. in their current orbits. ly since their formation. For example, Until recently, little provoked the idea It is widely accepted, however, that Earth’s moon is believed to have formed that the orbital configuration of the many of the smaller bodies in the solar within 30,000 kilometers (18,600 miles) planets has altered significantly since system—asteroids, comets and the plan- of Earth—but it now orbits at a distance their formation. But some remarkable ets’ moons—have altered their orbits over of 384,000 kilometers. The moon has developments during the past five years the past 4.5 billion years, some more dra- receded by nearly 100,000 kilometers in indicate that the planets may indeed matically than others. The demise of just the past billion years because of have migrated from their original or- Comet Shoemaker-Levy 9 when it col- tidal forces (small gravitational torques) bits. The discovery of the Kuiper belt has lided with Jupiter in 1994 was striking exerted by our planet. Also, many satel- shown that our solar system does not evidence of the dynamic nature of some lites of the outer planets orbit in lock- end at Pluto. Approximately 100,000 objects in the solar system. Still smaller step with one another: for instance, the icy “minor planets” (ranging between objects—micron- and millimeter-size in- orbital period of Ganymede, Jupiter’s 100 and 1,000 kilometers in diameter) terplanetary particles shaken loose from largest moon, is twice that of Europa, and an even greater number of smaller

58 Scientific American September 1999 Migrating Planets Copyright 1999 Scientific American, Inc. 50 from the well-separated, nearly circular 40 PLUTO and co-planar orbits of the eight other 30 major planets. Pluto’s is eccentric: during one complete revolution, the plan- 20 et’s distance from the sun varies from

(Millions of Years) (Millions of 10 OF SOLAR SYSTEM 29.7 to 49.5 astronomical units (one as- NEPTUNE 3:2 ORBIT

TIME SINCE FORMATION 2:1 ORBIT 0 tronomical unit, or AU, is the distance 0 10 20 30 40 50 between Earth and the sun, about 150 MEAN DISTANCE FROM THE SUN million kilometers). Pluto also travels 8 (Astronomical Units) AU above and 13 AU below the mean plane of the other planets’ orbits [see il- PLANETARY MIGRATION is shown in illustrations of the solar system at lustration at left]. For approximately the time when the planets formed (top left) and in the present (bottom left). The orbit of Jupiter is believed to have shrunk slightly, while the orbits of two decades in its orbital period of 248 Saturn, Uranus and Neptune expanded. (The inner planetary region was not years, Pluto is closer to the sun than significantly affected by this process.) According to this theory, Pluto was Neptune is. originally in a circular orbit. As Neptune migrated outward, it swept Pluto In the decades since Pluto’s discovery into a 3:2 resonant orbit, which has a period proportional to Neptune’s in 1930, the planet’s enigma has deep- (above). Neptune’s gravity forced Pluto’s orbit to become more eccentric and ened. Astronomers have found that inclined to the plane of the other planets’ orbits. most Neptune-crossing orbits are unstable—a body in such an orbit will either collide with Neptune or be ejected from the outer solar system in a relatively short time, typically less than 1 percent of the age of the solar system. But the particular Neptune-crossing orbit in which Pluto travels is protected from close approaches to the gas giant by a phenomenon called resonance libration. Pluto makes two revolutions around the sun during the time that Neptune makes three; Pluto’s orbit is therefore said to be in 3:2 resonance with Neptune’s. The relative motions of the two planets en- sure that when Pluto crosses Neptune’s orbit, it is far away from the larger plan- ) et. In fact, the distance between Pluto aph gr ( and Neptune never drops below 17 AU. CE A In addition, Pluto’s perihelion—its

URIE GR closest approach to the sun—always oc- A L curs high above the plane of Neptune’s ON;

DIX orbit, thus maintaining Pluto’s long-

DON term orbital stability. Computer simula- tions of the orbital motions of the outer planets, including the effects of their bodies occupy a region extending from derstand the formation of these putative mutual perturbations, indicate that the Neptune’s orbit—about 4.5 billion kilo- planets at such small distances from relationship between the orbits of Pluto meters from the sun—to at least twice their parent stars. Hypotheses for their and Neptune is billions of years old and that distance. The distribution of these origin have proposed that they accreted will persist for billions of years into the objects exhibits prominent nonrandom at more comfortable distances from future. Pluto is engaged in an elegant features that cannot be readily ex- their parent stars—similar to the dis- cosmic dance with Neptune, dodging plained by the current model of the so- tance between Jupiter and the sun—and collisions with the gas giant over the en- lar system. Theoretical models for the then migrated to their present positions. tire age of the solar system. origin of these peculiarities suggest the How did Pluto come to have such a intriguing possibility that the Kuiper Pluto: Outcast or Smoking Gun? peculiar orbit? In the past, this question belt bears traces of the orbital history of has stimulated several speculative and ad the gas-giant planets—specifically, evi- ntil just a few years ago, the only hoc explanations, typically involving dence of a slow spreading of these plan- Uplanetary objects known beyond planetary encounters. Recently, however, ets’ orbits subsequent to their formation. Neptune were Pluto and its satellite, significant advances have been made in What is more, the recent discovery of Charon. Pluto has long been a misfit in understanding the complex dynamics of several Jupiter-size companions orbiting the prevailing theories of the solar sys- orbital resonances and in identifying nearby sunlike stars in peculiarly small tem’s origin: it is thousands of times less their Jekyll-and-Hyde role in producing orbits has also focused attention on massive than the four gas-giant outer both chaos and exceptional stability in planetary migration. It is difficult to un- planets, and its orbit is very different the solar system. Drawing on this body

Migrating Planets Scientific American September 1999 59 Copyright 1999 Scientific American, Inc. 0.5 Orbit of Kuiper Belt Object Orbit of Pluto ORBITS IN RESONANCE WITH NEPTUNE'S ORBIT 0.4 4:3 3:2 5:3 2:1 T I B R O

O 0.3

Y ORBITS CLOSE TO T I NEPTUNE'S C I

R ORBIT T

N 0.2 E C C E

0.1 CE A GR URIE A

0 L 30 35 40 45 50 SEMIMAJOR AXIS OF ORBIT (Astronomical Units)

KUIPER BELT OBJECTS occupy a torus-shape region beyond Neptune’s orbit (right). The theory of planetary migration predicts that concentrations of these objects would be found in orbits in resonance with Neptune’s (inside blue brackets in illustration above). Recent observations indicate that about

one third of the Kuiper belt objects for which orbits are known (red dots) are ON

in 3:2 resonant orbits similar to Pluto’s (green cross). Few objects are expect- DIX

ed to be found in orbits that are very close to Neptune’s (shaded area). DON

of knowledge, I proposed in 1993 that from the giant planets’ orbits. But be- orbital energy and angular momentum Pluto was born somewhat beyond Nep- cause of their different masses and dis- to begin with, its orbit decayed only tune and initially traveled in a nearly cir- tances from the sun, this loss was not slightly. cular, low-inclination orbit similar to evenly shared by the four giant planets. The possibility of such subtle adjust- those of the other planets but that it was In particular, consider the orbital evo- ments of the giant planets’ orbits was transported to its current orbit by reso- lution of the outermost giant planet, first described in a little-noticed paper nant gravitational interactions with Nep- Neptune, as it scattered the swarm of published in 1984 by Julio A. Fernan- tune. A key feature of this theory is that planetesimals in its vicinity. At first, the dez and Wing-Huen Ip, a Uruguayan it abandons the assumption that the gas- mean specific orbital energy of the plan- and Taiwanese astronomer duo work- giant planets formed at their present dis- etesimals (the orbital energy per unit of ing at the Max Planck Institute in Ger- tances from the sun. Instead it proposes mass) was equal to that of Neptune it- many. Their work remained a curiosity an epoch of planetary orbital migration self, so Neptune did not gain or lose en- and escaped any comment among plan- early in the history of the solar system, ergy from its gravitational interactions et formation theorists, possibly because with Pluto’s unusual orbit as evidence of with the bodies. At later times, howev- no supporting observations or theoreti- that migration. er, the planetesimal swarm near Nep- cal consequences had been identified. The story begins at a stage when the tune was depleted of the lower-energy In 1993 I theorized that as Neptune’s process of planetary formation was al- objects, which had moved into the orbit slowly expanded, the orbits that most but not quite complete. The gas gravitational reach of the other giant would be resonant with Neptune’s also giants—Jupiter, Saturn, Uranus and planets. Most of these planetesimals expanded. In fact, these resonant orbits Neptune—had nearly finished coalesc- were eventually ejected from the solar would have swept by Pluto, assuming ing from the solar nebula, but a residu- system by Jupiter, the heavyweight of that the planet was originally in a near- al population of small planetesimals— the planets. ly circular, low-inclination orbit beyond rocky and icy bodies, most no larger Thus, as time went on, the specific Neptune. I calculated that any such ob- than a few tens of kilometers in diame- orbital energy of the planetesimals that jects would have had a high probability ter—remained in their midst. The rela- Neptune encountered grew larger than of being “captured” and pushed out- tively slower subsequent evolution of that of Neptune itself. During subse- ward along the resonant orbits as Nep- the solar system consisted of the scat- quent scatterings, Neptune gained or- tune migrated. As these bodies moved tering or accretion of the planetesimals bital energy and migrated outward. outward, their orbital eccentricities and by the major planets [see illustration on Saturn and Uranus also gained orbital inclinations would have been driven to page 56]. Because the planetary scatter- energy and spiraled outward. In con- larger values by the resonant gravita- ing ejected most of the planetesimal de- trast, Jupiter lost orbital energy; its loss tional torque from Neptune. (This ef- bris to distant or unbound orbits—es- balanced the gains of the other planets fect is analogous to the pumping-up of sentially throwing the bodies out of the and planetesimals, hence conserving the the amplitude of a playground swing solar system—there was a net loss of or- total energy of the system. But because by means of small periodic pushes at bital energy and angular momentum Jupiter is so massive and had so much the swing’s natural frequency.) The final

60 Scientific American September 1999 Migrating Planets Copyright 1999 Scientific American, Inc. maximum eccentricity would therefore two strongest resonances, the 3:2 and planetesimal population. Instead one provide a direct measure of the magni- the 2:1. Such orbits are ellipses with finds strong evidence of gaps and con- tude of Neptune’s migration. According semimajor axes of 39.5 AU and 47.8 centrations in the distribution. A large to this theory, Pluto’s orbital eccentrici- AU, respectively. (The length of the fraction of these KBOs travel in eccen- ty of 0.25 suggests that Neptune has semimajor axis is equal to the object’s tric 3:2 resonant orbits similar to Plu- migrated outward by at least 5 AU. average distance from the sun.) to’s, and KBOs in orbits interior to the Later, with the help of computer simu- More modest concentrations of trans- 3:2 orbit are nearly absent—which is lations, I revised this to 8 AU and also Neptunian bodies would be found at consistent with the predictions of the estimated that the timescale of migra- other resonances, such as the 5:3. The resonance sweeping theory. tion had to be a few tens of millions of population of objects closer to Neptune Still, one outstanding question re- years to account for the inclination of than the 3:2 resonant orbit would be mains: Are there KBOs in the 2:1 reso- Pluto’s orbit. severely depleted because of the thor- nance comparable in number to those Of course, if Pluto were the only ob- ough resonance sweeping of that region found in the 3:2, as the planet migration ject beyond Neptune, this explanation and because perturbations caused by theory would suggest? And what is the of its orbit, though compelling in many Neptune would destabilize the orbits of orbital distribution at even greater dis- of its details, would have remained un- any bodies that remained. On the other tances from the sun? At present, the verifiable. The theory makes specific hand, planetesimals that accreted be- census of the Kuiper belt is too incom- predictions, however, about the orbital yond 50 AU from the sun would be ex- plete to answer this question fully. But distribution of bodies in the Kuiper pected to be largely unperturbed and still on Christmas Eve 1998 the Minor Planet belt, which is the remnant of the pri- orbiting in their primordial distribution. Center in Cambridge, Mass., announced mordial disk of planetesimals beyond Fortunately, recent observations of the identification of the first KBO orbit- Neptune [see “The Kuiper Belt,” by Kuiper belt objects, or KBOs, have pro- ing in 2:1 resonance with Neptune. Two Jane X. Luu and David C. Jewitt; Sci- vided a means of testing this theory. days later the center revealed that an- entific American, May 1996]. Pro- More than 174 KBOs have been dis- other KBO was traveling in a 2:1 reso- vided that the largest bodies in the pri- covered as of mid-1999. Most have or- nant orbit. Both these objects have large mordial Kuiper belt were sufficiently bital periods in excess of 250 years and orbital eccentricities, and they may turn small that their perturbations on the thus have been tracked for less than 1 out to be members of a substantial pop- other objects in the belt would be negli- percent of their orbits. Nevertheless, ulation of KBOs in similar orbits. They gible, the dynamical mechanism of res- reasonably reliable orbital parameters had previously been identified as orbit- onance sweeping would work not only have been determined for about 45 of ing in the 3:2 and 5:3 resonances, re- on Pluto but on all the trans-Neptunian the known KBOs [see illustration on spectively, but new observations made objects, perturbing them from their opposite page]. Their orbital distribu- last year strongly indicated that the original orbits. As a result, prominent tion is not a pattern of uniform, nearly original identifications were incorrect. concentrations of objects in eccentric circular, low-inclination orbits, as would This episode underscored the need for orbits would be found at Neptune’s be expected for a pristine, unperturbed continued tracking of known KBOs in

A Planetary dynamicists (including myself) have System at Last? already determined that the orbital configuration of this putative system is at best marginally stable.The n April 1999 astronomer R. Paul SUN system’s dynamical stability would IButler of the Anglo-Australian Ob- improve greatly if there were no servatory and his colleagues an- middle companion. This is note- nounced the discovery of what is ORBIT OF worthy, as the observational evi- apparently the first known case JUPITER dence for the middle companion is of a planetary system with several weaker than that for the other two. Jupiter-mass objects orbiting a sun- The Upsilon Andromedae system like star. (Previously, only systems appears to contradict all the theo- with one Jupiter-mass companion rized mechanisms that would cause had been detected.) The star is Up- giant planets to migrate inward silon Andromedae; it is approxi- UPSILON ANDROMEDAE SYSTEM is believed to from distant birthplace orbits.If disk- mately 40 light-years from our so- include three Jupiter-mass companions orbiting the protoplanet interactions caused the lar system and is slightly more mas- star (top). Their theorized orbits are much tighter orbits to decay, the more massive sive and about three times more than Jupiter’s orbit in our solar system (bottom). ON planet would most likely be the ear- luminous than our sun. liest born and hence found at the DON DIX The astronomers say their analy- shortest distance from the star— sis of the observations shows that Upsilon Andromedae harbors contrary to the pattern in the Upsilon Andromedae system. If only three companions.The innermost object is at least 70 percent as the innermost and outermost companions are real, the system massive as Jupiter and is moving in a nearly circular orbit only 0.06 could represent an example of the planet-planet scattering model AU—or about nine million kilometers—from the star. The outer- in which two massive planets migrate to nearby orbits,then gravi- most companion object is at least four times as massive as Jupiter tationally scatter each other,eventually yielding one in a close,near- and travels in a very eccentric orbit with a mean radius of 2.5 AU— ly circular orbit and the other in a distant,eccentric orbit.A difficul- half the radius of Jupiter’s orbit.The intermediate object is at least ty with this scenario is that the more massive companion would be twice as massive as Jupiter and has a moderately eccentric orbit expected to evolve to the small orbit and the less massive one to with a mean radius of 0.8 AU. the distant orbit—again,contrary to the characteristics of the Up- If confirmed, the architecture of this system would pose some silon Andromedae system. interesting challenges and opportunities for theoretical models Could this system represent a hybrid case of these two scenar- of the formation and evolution of planetary systems.A number of ios—that is,orbital decay caused by disk-protoplanet interactions

order to map their orbital distribution lar system. In other words, the planetary disk. If the torques exerted on the pro- correctly. We must also acknowledge migration occurred in the early history toplanet by the disk matter just inside the dangers of overinterpreting a still of the solar system but during the later the planet’s orbit and by the matter just small data set of KBO orbits. stages of planet formation. The total beyond it were slightly unbalanced, In short, although other explanations mass of the scattered planetesimals was rapid and drastic changes in the planet’s cannot be ruled out yet, the orbital dis- about three times Neptune’s mass. The orbit could happen. But again, this the- tribution of KBOs provides increasingly question arises whether even more dras- oretical possibility received little atten- strong evidence for planetary migra- tic orbital changes might occur in plane- tion from other astronomers at the tion. The data suggest that Neptune was tary systems at earlier times, when the time. Having only our solar system as born about 3.3 billion kilometers from primordial disk of dust and gas contains an example, planet formation theorists the sun and then moved about 1.2 bil- more matter and perhaps many proto- continued to assume that the planets lion kilometers outward—a journey of planets in nearby orbits competing in were born in their currently observed almost 30 percent of its present orbital the accretion process. orbits. radius. For Uranus, Saturn and Jupiter, In the past ﬁve years, however, the the magnitude of migration was small- Other Planetary Systems? search for extrasolar planets has yielded er, perhaps 15, 10 and 2 percent, re- possible signs of planetary migration. By spectively; the estimates are less certain n the early 1980s theoretical studies measuring the telltale wobbles of nearby for these planets because, unlike Nep- Iby Peter Goldreich and Scott Tre- stars—within 50 light-years of our solar tune, they could not leave a direct im- maine, both then at the California Insti- system—astronomers have found evi- print on the Kuiper belt population. tute of Technology, and others conclud- dence of more than a dozen Jupiter-mass Most of this migration took place ed that the gravitational forces between companions in surprisingly small orbits over a period shorter than 100 million a protoplanet and the surrounding disk around main-sequence stars. The ﬁrst years. That is long compared with the of gas, as well as the energy losses putative planet was detected orbiting the timescale for the formation of the plan- caused by viscous forces in a gaseous star 51 Pegasi in 1995 by two Swiss as- ets—which most likely took less than medium, could lead to very large ex- tronomers, Michel Mayor and Didier 10 million years—but short compared changes of energy and angular momen- Queloz of the Geneva Observatory, who with the 4.5-billion-year age of the so- tum between the protoplanet and the were actually surveying for binary stars.

62 Scientific American September 1999 Migrating Planets Copyright 1999 Scientific American, Inc. masses of the stars’ companions. Most the planet would be virtually locked to of the candidate planets have minimum the inward flow of gas accreting onto in the case of the innermost object and masses of about one Jupiter-mass and the protostar and might either plunge mutual gravitational scattering for the oth- orbital radii shorter than 0.5 AU. into the star or decouple from the gas er two companions? Perhaps entirely differ- What is the relationship between these when it drew close to the star. The sec- ent formation and evolution processes are objects and the planets in our solar sys- ond mechanism is interaction with a also involved,such as the fragmentation of tem? According to the prevailing model planetesimal disk rather than a gas disk: the protostellar gas cloud that is thought to of planet formation, the giant planets in a giant planet embedded in a very mas- produce multiple-star systems and brown our solar system coalesced in a two-step sive planetesimal disk would exchange dwarf companions. process. In the first step, solid planetesi- energy and angular momentum with the If only the innermost and outermost mals clumped together to form a proto- disk through gravitational scattering and companions are real, the system would be planetary core. Then this core gravita- resonant interactions, and its orbit would architecturally similar to classic triple-stellar tionally attracted a massive gaseous en- shrink all the way to the disk’s inner systems consisting of a tight binary with a velope from the surrounding nebula. edge, just a few stellar radii from the star. distant third star in an eccentric orbit. At This process must have been completed The third mechanism is the scattering present, we have only speculations for the within about 10 million years of the for- of large planets that either formed in or Upsilon Andromedae system. More obser- mation of the solar nebula itself, as in- moved into orbits too close to one an- vations and further analysis should help ferred from astronomical observations other for long-term stability. In this pro- firm up the evidence for the number of of the lifetime of protoplanetary disks cess, the outcomes would be quite un- companions and for their masses and orbital parameters. around young sunlike stars. predictable but generally would yield The discovery methods employed so far At distances of less than 0.5 AU from very eccentric orbits for both planets. In are unable to detect planetary systems like a star, there is insufficient mass in the some fortuitous cases, one of the scat- our own because the stellar wobble from primordial disk for solid protoplane- tered planets would move to an eccentric Earth-size planets in close orbits—or from tary cores to condense. Furthermore, it orbit that would come so near the star at Jupiter-size planets in more distant orbits— is questionable whether a protoplanet its closest approach that tidal friction is below the observable threshold. There- in a close orbit could attract enough would eventually circularize its orbit; the fore, it would be premature to leap to con- ambient gas to provide the massive en- other planet, meanwhile, would be clusions about the astronomical frequency velope of a Jupiter-like planet. One rea- scattered to a distant eccentric orbit. All of Earth-like planets.Our understanding of son is simple geometry: an object in a the mechanisms accommodate a broad the origin of the recently identified com- tight orbit travels through a smaller range of final orbital radii and orbital panions to sunlike stars is sure to evolve volume of space than one in a large or- eccentricities for the surviving planets. and thereby expand our understanding of bit does. Also, the gas disk is hotter These ideas are more than a simple our own solar system. —R.M. close to the star and hence less likely to tweak of the standard model of planet condense onto a protoplanetary core. formation. They challenge the widely These considerations have argued held expectation that protoplanetary against the formation of giant planets disks around sunlike stars commonly Their observations were quickly con- in very short-period orbits. evolve into regular planetary systems like firmed by Geoffrey W. Marcy and R. Instead several theorists have suggest- our own. It is possible that most planets Paul Butler, two American astronomers ed that the putative extrasolar giant are born in unstable configurations and working at Lick Observatory near San planets may have formed at distances that subsequent planet migration can Jose, Calif. As of June 1999, 20 extraso- of several AU from the star and subse- lead to quite different results in each sys- lar planetary candidates have been iden- quently migrated inward. Three mecha- tem, depending sensitively on initial tified, most by Marcy and Butler, in nisms for planetary orbital migration disk properties. An elucidation of the search programs that have surveyed al- are under discussion. Two involve disk- relation between the newly discovered most 500 nearby sunlike stars over the protoplanet interactions that allow extrasolar companions and the planets past 10 years. The technique used in planets to move long distances from in our solar system awaits further theo- these searches—measuring the Doppler their birthplaces as long as a massive retical and observational developments. shifts in the stars’ spectral lines to deter- disk remains. Nevertheless, one thing is certain: the mine periodic variations in stellar veloci- With the disk-protoplanet interactions idea that planets can change their orbits ties—yields only a lower limit on the theorized by Goldreich and Tremaine, dramatically is here to stay. SA

The Author Further Reading

RENU MALHOTRA did her undergraduate studies at the Indi- Newton’s Clock: Chaos in the Solar System. Ivars Peterson. an Institute of Technology in Delhi and received a Ph.D. in physics W. H. Freeman and Company, 1993. from Cornell University in 1988. After completing postdoctoral re- Detection of Extrasolar Giant Planets. Geoffrey W. Marcy search at the California Institute of Technology, she moved to her and R. Paul Butler in Annual Review of Astronomy and Astro- current position as a staff scientist at the Lunar and Planetary Insti- physics, Vol. 36, pages 57–98; 1998. tute in Houston. In her research, she has followed her passionate in- Dynamics of the Kuiper Belt. Renu Malhotra et al. in Proto- terest in the dynamics and evolution of the solar system and other stars and Planets IV. Edited by V. Mannings et al. University of planetary systems. She also immensely enjoys playing with her four- Arizona Press (in press). Available at http://astro.caltech.edu/~ year-old daughter, Mira. vgm/ppiv/preprints.html on the World Wide Web.