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Cosmic Reflections Evolution of the Solar System: The role of chaos.
The Urantia Book's story about the origin of our solar system is at variance with the popular, and often dogmatic, text-book accounts. Current thought indicates that, in any account of origins, there may be a high degree of uncertainty.
Commencing in the seventeenth century with Isaac Newton's proclamation of his laws describing the motion of material bodies and gravity, a new era opened up in the study of the orbits of celestial bodies. Using Newton's laws to explore celestial mechanics, astronomers soon showed that these deceptively simple mathematical statements appeared to capture the essence of how the universe truly works. As a result of their application, it was possible to envision a completely deterministic universe in which the entire past and future lay encompassed within this mathematical framework. The clock could be turned back or forward with ease.
It may perhaps have been good fortune that many of the known properties of the solar system are reasonably well described by these Newtonian concepts. But whether this is inevitable because the solar system, and others like it, are the only kinds of system that have sufficient stability to exist for any extended period is another question.
The complexity of what is known as the "three body problem" is illustrated in Fig. 1 which demonstrates the complex motions possible in a system of only three interacting gravitating bodies. An examination of Fig. 1 makes it obvious that the point and angle of entry of the small body onto the system will vastly alter the trajectory it will follow and that, indeed, the complexity of even this simple system is such that it borders on the unpredictable. Unpredictability is even better illustrated in Fig. 2--the billiard ball effect--in which it should be obvious that even a minute alteration in initial conditions would vastly effect the subsequent behavior of the system. For the astronomer, it is this kind of unpredictability that is included under the heading of "chaotic motion."
The development of the clockwork universe concept was largely due to a brilliant French mathematician, Pierre-Simon de Laplace who formulated an idealized mathematical solar system that remained stable despite small deviations in the eccentricities and inclinations of planetary orbits. Laplace concluded that these small perturbations could not accumulate to wreak havoc on the solar system's arrangement. To him, all of nature functioned like his solar system--as a clockwork. In his classic statement on determinism, he said, "Assume an intelligence that, at any given moment, knows all the forces that animate nature as well as the momentary positions of all things of which the universe consists, and further that it is sufficiently powerful to perform a calculation based on these data. It would then include in the same formulation, the motions of the largest bodies in the universe and those of the smallest atoms. To it, nothing would be uncertain. Both future and past would be present before its eyes."
Naturally, Laplace's pronouncements (which were backed up by his massive five volume treatise on celestial mechanics) caused wide-ranging discussion. Some asked questions such as, "Imagine a large rock precariously poised on the top of a mountain peak. Toppled by the slightest shove, the rock could easily trigger a massive avalanche in the course of its descent down the mountain's slope--do such instabilities exist within the solar system?" Laplace did not think so, but when he tried to tame the moon's motion, he failed to account for all the details of its orbit. So do multifarious gravitational interactions also generate cantankerous mathematical behavior?
From the time of Newton, it was not unusual for large prizes to be offered for the solution of important mathematical problems. It was such a contest for a large cash prize to celebrate the sixtieth birthday of the King of Sweden on January 21, 1889, that tempted the most eminent mathematicians of the day to present their papers on one of the four topics suggested by the award committee. Among them was another French mathematician, Henri Poincare, the eventual winner, whose entry included the three body problem mentioned in our Fig.1. and concluded that although the equations representing three gravitationally interacting bodies may yield a well-defined relationship between time and position, there exists no all-purpose computational shortcut--no magic formula--for making accurate predictions far into the future. In other words the series that arise out of perturbation theory typically diverge. Thus there was plenty of room for the unpredictable ("chaos") in a Newtonian system, and the question of stability could not be settled by examining the divergent series associated with solutions of the equations of motion for the solar system.
Despite Poincare's findings, the deterministic clockwork universe remained firmly embedded in twentieth century philosophy. A paper published in 1963 by Vladimir Arnol'd provided proof than any solar system, despite its potential for chaos, will, for all practical purposes, remain quasi-periodic, hence stable--provided that the masses, inclinations, and eccentricities of the planets are sufficiently small.
The outstanding question to be asked about Arnold's hypothesis is what constitutes being "sufficiently small?" Up until the 1970's, investigations on the motions of Jupiter, Saturn,
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