MYTHS ARE HISTORY
On the Ultimate Instability of
the Solar System
On the Ultimate Instability of the Solar System
Although modern theorems of cosmological equilibrium condition the expectation that uniform processes have always dominated planetary systems and will always continue to do so, the long-term stability of the Solar System has been a subject of great inquiry and profound contention in astronomy and mathematics since the time of Plato, and is commonly regarded to be one of the oldest problems in theoretical physics.
While the positions of the planets appear to be more or less stable in most observations made since the early Iron age, previous observations made during the Bronze age are often widely divergent and far less capable of predictive accuracy with regard to the solar system of today. [...] — If the astronomer-priests of the Bronze age indeed theorized that interactions among the ‘wandering stars’ above were sometimes responsible for catastrophic events on Earth below, their efforts would’ve been first focused on finding some regularity in the motion of the planets, so that their movements with regard to Earth (vis a vis the backdrop of fixed stars) could be more readily predicted.
The advent of fixed cultural settlements (no matter how big or small) enabled the construction and proper utilization of basic astronomical observation tools — such as gnomons and water clocks. Gnomons and water-clocks were commonly used in tandem to precisely time the proper days of their annual New Year festivals — as well as to carefully track the orbital periods and relative positions of the planets. Examples recovered from China, India, Babylon, Egypt, Iran, Greece, Rome, and elsewhere, demonstrate that both tools were in use during the Bronze Age by the same myth-making peoples who perpetuated equinoctial new years festivals around the globe.
The early Pythagoreans were the first to find the order of the planets visible to the naked eye. An early astronomical system positing that the Earth, Moon, Sun, and planets revolve uniformly around an unseen "Central Fire" which powered their motions was developed by Pythagorean philosopher Philolaus around the fifth century BC. The first coherent system in which celestial bodies move in circles, it was also the first to model Earth itself as a planet, insightfully demonstrating that the apparent motion of the heavenly bodies was in part due to the motion of the observer.
Democritus (c. 460-370 BC) argued that other planetary systems existed outside of ours, and emphatically asserted that they were subject to destructive collisions: “there are innumerable worlds of different sizes. In some there is neither sun nor moon, in others they are larger than in ours and others have more than one. These worlds are at irregular distances, more in one direction and less in another, and some are flourishing, others declining. Here they come into being, there they die, and they are destroyed by collision with one another. Some of the worlds have no animal or vegetable life nor any water."
Eudoxus of Cnidus (c. 400-347 BC) devised the first geocentric mathematical construct of the solar system, with sets of concentric spheres circling the Earth at different paces functioning as computational devices for representations of the motions of the Sun, Moon and the planets. Eudoxus’ model was later refined and expanded by Callippus of Cyzicus (c. 370-300 BC); and subsequently borrowed and further expanded by Aristotle (c.384-322 BC), who also attributed a physical existence to the series of concentric spheres, suggesting they were composed of some “perfect” and “transparent” material.
Heraclides of Pontus (c. 388-315 BC) is said to be the first Greek to propose that the Earth rotates on its axis, from west to east, once every 24 hours, contradicting Aristotle's teachings. Heraclides further noted that the irregular movements of the planets could be explained if the Earth is in motion while the Sun remains still — and his suggestion that Mercury and Venus orbit the Sun rather than the Earth may indicate that Heraclides was among the first to propose a heliocentric solar system.
Some of the Stoic philosophers influenced by Heraclitus posited that the cosmos abides in a state of flux, pulsates in size, and undergoes periodic upheavals and conflagrations.
Aristarchus of Samos (c. 310-230 BC) was the first known to have openly proposed a heliocentric system based on his own personal observational data. Earth as a planet rotates daily on axis and revolves annually around the Sun at the center.— Further proofs for a heliocentric system were developed by Seleucus of Seleucia (c 190-150 BC) during the following century.
In the era of Apollonius of Perga (c. 240-190 BC), Hipparchus of Nicaea (c. 190-120 BC) and Ptolemy of Alexandria (c. 100-170 AD), however, a geocentric model was still in wide use. The predictive model at that time was a combination of uniform circular motions, called epicycles and deferents, which were in continual need of adjustment in order to conform to the actual observed courses of the planets. Like Eudoxus’ system, Ptolemy’s was viewed more as a calculational device to account for observed phenomena, rather than a representation of the actual physical system. Ptolemy’s model was, in effect, a set of systems, with one for each of the major planets. The Sun alone did not move in epicycles, and the motions of Mercury, Venus, Mars, Jupiter and Saturn were all linked to the motion of the Sun. The use of Ptolemy’s invented equant points allowed astronomers to predict the future positions and ecliptic latitudes of the planets with respect to the Zodiac.
Despite its complexity, the Ptolemaic system remained the prevailing authoritative model for many centuries to come. Over the next several centuries, however, it drew increasing criticism on account of its inability to describe the actual physical properties of the solar system. Among the most notable critiques were those made by the Neoplatonist Proclus (5th c AD), the Islamic philosopher Averroes (Abu'l Walid Muhammad ibn Rushd, 12th c AD), the Jewish theologian Moses Maimonides (12th c AD), and the Catholic apologist Thomas Aquinas (13th c AD).
In addition, during this same interval several Indian astronomers (including Aryabhata (5th c AD)) began proposing heliocentric models, positing that the Earth should be numbered among the rotating planets revolving around the Sun. — From the 12th through 15th centuries of the common era, several European mathematicians and astronomers (including Robert Grosseteste (1175-1253) and Nicole Oresme (d. 1382) revived the earlier position of Heraclides and Aristarchus, proposing that the Earth’s rotation on its own axis (and the not the motion of the Sun around the Earth) was the real cause of day and night.
Nicolas of Cusa (c. 1401-1464), hypothesizing that some statements of ancient writers may be explained by their having seen a sky different from what was seen in his own day, claimed that heavenly motions do not have stability as an inherent quality. He rejected the notion that the orbits of the planets were perfectly circular, and revived the older heliocentric arguments of the Greeks and Romans. He was also among those who proposed the Earth rotates on its own axis, and that other planetary systems likely abounded outside of our own.
Similarly, Giordano Bruno (c. 1548-1600), in his last and greatest work, theorized that since we possess no records which can prove that all the heavenly bodies had always occupied exactly the same positions in the past, denied that planetary motions are rigidly regular, and hence disavowed the general stability of our solar system. Bruno, like Democritus and Cusa, also argued in favor of the existence of a multitude of other planetary systems outside of ours.
Copernicus (1473-1543) was among the first in more modern times to devise a model of the solar system in realist terms. Acknowledging Philolaus’ model of Earth as a revolving planet, Copernicus also asserted the rotation of Earth around its axis, and positioned the Sun in the center of the system (ala Heraclides and Aristarchus) — and even dared to model the Moon as orbiting the Earth. Placing Earth around the Sun with the other planets not only eliminated of the problem of modeling planetary retrogrades, it also allowed for far more accurate measurements of the distances between Earth and the other heavenly bodies. All in all, by giving a mathematical structure to the heliocentric theory, Copernicus’ model represented a direct challenge to Aristotle’s physics as well as the literal interpretation of several passages of scripture; and it was thus on these grounds that Copernicus’ model was rejected by both Catholic and Protestant theologians.
In the early 1600s, Johannes Kepler (1571-1630) laid the groundwork for modern celestial mechanics by formulating the laws of planetary motion from the observed motions of the planets. Assimilating the lessons of Copernicus and the measured observations of Tycho Brahe (1546-1601), Kepler placed the Sun at the center of the system and showed that the planets’ trajectories described, not perfect circles, but rather ellipses around the Sun. At the end of a revolution, each planet found itself back where its elliptical course had begun, and so kept retracing the same orbital ellipse. — More controversially, Kepler also believed that world history was divisible into a series of stages, each of which had been demarcated by particular conjunctions of Jupiter and Saturn.
Kepler’s ideal vision of a perfectly stable system in which all orbits were periodic did not remain unchallenged for very long, however. Fellow Copernican realist Galileo Galilei (1564-1642) famously denied the that the heavens were immutable, stating that cosmological theories about the structure of the solar system must stand or fall on historical evidence and the traditions of the ancients. — In addition, many of the new telescope-based astronomers noted that the observed positions of Jupiter and Saturn unpredictably deviated from their mathematically-modeled positions by some 30 minutes of arc. This inexplicable dynamic subsequently became known as the ‘Great Inequality.’
Isaac Newton’s (1643-1727) mathematical description of gravitation and the basic laws of planetary motion seemed to arrive at a relatively simple set of equations to determine the motions of the planets. The predictability of planetary motions offered by Newton’s equations was, moreover, largely responsible for the general acceptance of his theory of gravitation. Newton himself, however, had grave doubts about the long-term stability of the solar system. According to his own theory, Newton admitted that the gravitational pull among the several members of the solar system would tend to modify their orbits in unpredictable ways over time: “the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted, which may have arisen from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation” (Newton, Opticks 378).
Newton believed that the solar system was ultimately unstable, and that these small mutual interactions would gradually degrade the regular arrangement of the planets’ orbits, which could lead eventually to a collision between planets, the ejection of a planet to interstellar space, or perhaps even the incineration of a planet by the Sun. In his view, perturbations among the planets were strong enough to destroy the solar system as we know it — and , as such, divine intervention must be required from time to time to restore the planets’ well-spaced orbits back to the places we observe today — a doctrine based not on scientific data but rather on Newton’s own faith in a providential order. He categorically denied that any similar scenario had ever before occurred, however, and in unpublished writings strove to discredit references to astronomical and other natural events in myth, as well as the historical evidence presented by contemporary theories for earlier changes in the solar system.
Since then, mathematicians and astronomers have continued searching for evidence and proof for the long-term stability of planetary motions. Meanwhile, speculations on cosmic cataclysms became increasingly commonplace. More and more scholars began to doubt that the universe had been created only once and for forever. — Newton’s contemporary and rival Gottfried Leibniz (1646-1716) sneered at Newton’s conception of a God so incompetent as to be reduced to miracles in order to rescue his machinery from collapse. Furthermore, Newton’s own student, William Whiston (1667-1752), in his book entitled New Theory of the Earth, argued against the stability of the solar system, contending that the creation myth recounted in Genesis referred to a process of progressive creation through several cosmic stages.
That the problem of solar system stability was indeed a genuine matter of inquiry was further demonstrated by Edmund Halley (1656-1742), who (following Kepler’s lead) re-analyzed the Chaldean astronomical observations of the late Bronze and early Iron ages that had been reproduced by Ptolemy, concluding that Jupiter and Saturn had formerly been much closer together, and that presently Saturn was moving away from the Sun while Jupiter was moving closer. — What had encouraged Halley’s study was that the positions of Jupiter and Saturn in particular still could not be accurately modeled by Newton’s equations any more than they could by Kepler’s.
It was Pierre-Simon Laplace (1749-1827) who noted that the predictions did not take into account the influence of Saturn on Jupiter's orbit, and vice versa. Laplace realized that the perturbations between their orbital periods accumulated over a much longer interval, permitting an exchange of energy and angular momentum between the two planets. many times larger than anyone’s estimations had indicated.
This discovery strongly affected Laplace's views regarding determinism, as reflected his well-known statement: “The present state of the system of nature is evidently a consequence of what it was in the preceding moment ...” (Laplace, Oeuvres Complete de Laplace Vol. 8, 144-145). Dispensing with Newton’s hypothesis of divine intervention would thereafter become a major activity of Laplace's scientific life. He felt the need in particular to refute Newton’s argument that the planets and their satellites rotating counterclockwise is proof of divine providence. Laplace instead insisted that the motions of the Earth were indeed alterable, being subject to unpredictable forces, including the impacts of comets and meteorites, and that one should study the historical evidence for such events. In return, he (and Joseph-Louis Lagrange (1736-1813)) devised analytic proofs demonstrating that in their masses, inclinations and eccentricities of orbit, the planets do not in fact move one and the same way, as both Kepler and Newton had argued, but rather move quasiperiodically instead.
After the work of Laplace and Lagrange, it was generally taken for granted that the motions of the planets were indeed quasiperiodic, and thus efforts in celestial mechanics in the nineteenth century were largely devoted to the construction of quasiperiodic solutions for all the bodies of the Solar System. This approach was questioned when Henri Poincare (1854-1912) demonstrated that all forgoing proofs of the solar system’s stability were actually all based on approximations that are not completely accurate at this time, and thus do not prove constitute proof of its stability.
Another century later, remarkable advances in digital computers, the development of new mathematical techniques, and the application of nonlinear dynamics led to the discovery of a number of examples of ongoing dynamical chaos in our solar system. Gerald Jay Sussman (b. 1947) and Jack Wisdom (b. 1953), and most famously Jacques Laskar (b. 1955), using updated methods developed by Laplace and Lagrange, performed numerical integrations of the planets’ orbits and found that the whole system is ultimately chaotic. The same holds true for both inner planets as well as the outer ones. The perturbations and variations in the planets’ orbits are not quasiperiodic after all, but are instead, rather, decidedly nonlinear, ultimately rendering the prevailing planetary order unstable over long periods of time. The resonances between them are extremely weak and hence, theoretically, could be easily disrupted.
— There is thus no hope of precisely tracking the real motion of the solar system over longer periods of future time. Mathematical integrations of the solar system over millions or billions of years can thus only be considered indicators of its possible behavior, and are ultimately incapable of predicting its actual future motions. This also means that the traditional tools of celestial mechanics, which aim at uniform solutions given from idealized initial conditions, will remain incapable of predicting any forthcoming catastrophic events.
Moreover, the question of the maximum possible variations of planetary orbits over past ages now becomes even more difficult to answer as well. For if the solar system is unstable at present in its current form, it becomes much easier to suppose that a chaotic, even catastrophic evolution of planetary orbits was an ongoing process in the structuring of the system, even long after the early stages of its initial formation. — Future attempts to account for the mythic history of our system’s structure, as such, might look instead to catastrophe theory, and the tenets of ‘Punctuated Equilibrium,’ and invoke the basic principles of dynamical dissipative structures, instead of falling back on old suppositions of uniform equilibrium.