© 1997 Ken Glasziou
© 1997 The Brotherhood of Man Library
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, Uranus, and Pluto ignored the possible effects of the inner planets. The planet Mercury revolves around the sun in 88 days whereas Pluto requires a little more than 1,000 times longer. Any direct calculation has to proceed in increments small enough to follow each planet and because nothing much happens in mere thousands of years, the evolution of orbits has to be tracked for many millions of years to yield meaningful insights. In principle, a sufficiently powerful computer could step through the necessary calculations but in practice, numerical integrations of the whole solar system required such enormous amounts of computer time that simplification and approximation became essential. Up to 1983, no one had traveled more than five million years into the solar system’s future, and those who had traveled this far had seen no signs of irregularity.
A change in technology that occurred in the early eighties was primarily due to Gerard Sussman who seized upon the idea of designing a computer specifically for the task of doing the calculations required in celestial mechanics. This was followed up by collaborative work with astronomer, Jack Wisdom, to design mathematical techniques for exploiting the new technology.
Along with advancing technology, there arose more and more evidence for the occurrence of chaos (in the mathematical sense) in the celestial mechanics of the solar system. Wisdom and Sussman were able to identify elements of chaos in the orbit of Pluto, and Jacques Laskar, of the Bureau des Longitudes, Paris, came up with a study of the whole solar system (except Pluto) and showed that starting with as little a difference as 100 meters in the Earth’s position at a given moment, it would be impossible to specify where it would be in its orbit 100 million years later. At the University of Toronto in Canada, Tremaine, Duncan, and Quinn carried out work of importance to Urantia Book readers who have taken an interest in the ‘missing’ planet problem. In their studies of planetary orbits lying between Uranus and Neptune, they found that in roughly half of the cases studied, the orbit became sufficiently chaotic to ensure that, during some part of a five billion year period, any planetary body in that orbit would be likely to be ejected from the solar system.
In 1992, Wisdom and Sussman re-entered the fray with their second custom-built computer with which they were able to trace the evolution of the entire solar system over 100 million years intervals. In doing so, they confirmed the earlier work indicating the chaotic motion of Pluto and Laskar’s more general result that the solar system, as a whole, displays elements of chaotic behavior. Models made by Gerald Quinlan of a hypothetical solar system containing just the four planets, Jupiter, Saturn, Uranus, and Neptune, showed that in his simulations of more than fifty randomly adjusted “solar systems,” a majority gave evidence for the development of chaotic behavior.
This recent evidence raises the question of whether the particular distribution of planets in our solar system is one of only a limited number capable of enduring because of having exceptional relative stability. Opinion differs about its having room for an additional planet without becoming de-stabilized. Some researchers suspect that any additional planet would be at risk of being ejected from the system. Others speculate that, several billion years ago, the solar system did actually hold additional planets, perhaps the size of our moon or Mars, that were subsequently ejected.
One of the more dramatic consequences of the chaotic evolution of planetary orbits is the effect it may impose upon the angle of tilt of a planet’s axis. For the earth, the moon acts as a stabilizing influence. However with inner planets like Mars and Venus, simulations indicate the tilt angles may have evolved chaotically. If so, an alternative explanation is offered for the peculiarity of Venus which rotates about its axis in an opposite direction to its orbital motion. Laskar and his colleagues argue that, because of chaotic effects, the axis of rotation of Venus could have suffered severe tilting to the point that it actually flipped over, thus giving a spin contrary to its orbital motion. If so, Venus is simply “upside down.”
Among the concluding remarks in his recent book, Ivars Peterson asks: “How much of a role did chaos play in the formation of the solar system? Did the solar system settle down into its present configuration (with well-spaced planets following nearly circular orbits lying roughly in the same plane) within its first few million years? Or has it gradually evolved to its present configuration over the last five billion years? Were there other planets that have since been ejected? What is the Earth’s true trajectory? Is it gradually nearing the sun, eventually to be swallowed up, or is it slowly drifting away into the depths of interstellar space? . . . What seems clear now is that the solar system is, on astronomical scales, no simple, well-regulated clock.”
The Urantia Book (UB 57:5.7) indicates that there were actually twelve planets present soon after the birth of the solar system. If chaos in the solar system is a reality, then the number of planets may have decreased through some being ejected. But perhaps it is still possible for new planets to be discovered. An alternative hypothesis is that what were once planets in their own right have since become moons of other planets—or the reverse. Our moon is larger than the planet Pluto. Presumably if it escaped into a stable orbit, it would then be classified as a planet.
As bigger and better computers come on line, perhaps some of the problems arising from The Urantia Book’s account of the solar system’s evolution will be clarified. One of the more interesting suggestions coming from those who support the concept of chaos is that the “text book” account of its present configuration system having become stabilized in the first few million years may be incorrect. Perhaps convergence of the book’s account and scientific opinion may yet occur.
Strange Attractor
A strange attractor is a phase-space graph that charts the trajectory of a system in chaotic motion. A system in chaotic motion is completely unpredictable—given the configuration of the system at any one point in time, it is impossible to predict with certainty how it will end up at a later point in time. However, the motion of the chaotic system is not completely random, as evidenced by the general pattern of the trajectory in the interactive chart above. (Dynamic Mathematics,© 2018 Juan Carlos Ponce Campuzano)