FEATURE ARTICLE
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
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 interactions 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?
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, 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 large-scale 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 giant 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 short-period 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.
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