Are Planetary Systems Filled to Capacity?
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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]. +VQJUFSQFSJPESBUJP 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 OVNCFSPGPCKFDUT UIPVTBOET Many of the objects in the Kuiper belt have their orbits locked in a sta- ble 2:3 mean-motion resonance with Neptune. They orbit the Sun twice for every three orbits of this planet. PSCJUBMTFNJNBKPSBYJT BTUSPOPNJDBMVOJUT Such objects are called plutinos, after Pluto, the first one discovered. Some Figure 2. Resonant effects can be clearly seen in the radial distribution of the asteroids. Some of them, including Pluto, cross inside 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 the orbit of Neptune, but the geom- is bounded by the 4:1 and 2:1 orbital resonances with Jupiter. The stable 3:2 and 1:1 resonances etry of their resonant orbits keeps account, respectively, for the Hilda family of asteroids and the Jupiter Trojans. The semimajor them from making close approaches axis is one-half the long dimension of an object’s elliptical orbit. One astronomical unit is the to the planet and accounts for their Earth-Sun distance. (Distribution of asteroids courtesy of the Minor Planet Center.) survival. Thousands of small worlds called early solar system, close encounters those planets migrated outward, to Trojan asteroids share Jupiter’s orbit of small icy bodies with the growing conserve the total angular momentum. around the Sun, leading or following giant planets populated the distant But the much more massive planet Ju- the planet by about 60 degrees.