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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

This article is published in cooperation with NASA’s online Astrobiology Magazine (

Figure%201.%20Hypothetical%20planetary%20system%20in%20the%20makingClick to Enlarge ImageIn 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 Pierre-Simon Laplace had concluded that the solar system requires no such guiding hand but is, in fact, naturally self-correcting 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 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.

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