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Our Solar System seems well planned, with a neat set of four little inner planets fenced in by the Sun and the asteroid belt, with an outer region populated by a stately progression four gas giants and bounded on the outside by the Kuiper Belt.  The largest gas giant, Jupiter, with a mass of 318 Earth masses, is 5.2 AU from the Sun (where 1 AU is Earth’s average orbital radius).  Next comes Saturn with a mass of 95 Earth masses, which orbits at 9.5 AU.  Uranus, the lightweight of the gas giants with a mass of 14 Earth masses, orbits at 19.6 AU. The outermost gas giant Neptune , with a mass of 17 Earth masses, orbits at 30 AU.

The regularity of the Solar System’s planetary orbits was noted as early as 1715, and in 1768 Johann Bode proposed a “law” stating that the orbits of the planets in AU could be predicted by a mathematical relation, which we can now write as
R_n = [4 + (3/2) 2ⁿ]/10, where n=1, 2, 3, …  for the planets from Venus to Neptune, with n=4 corresponding to a “missing planet” at roughly the orbital radius of the asteroid belt..  The orbit of Mercury (n=0) doesn’t quite fit the systematics of the model and has a value of R₀=4/10.  But is this regularity an accident or an indication of some systematic natural process?   It now looks like an accident, in that a new model of planetary orbits suggests that a chaotic catastrophe in the early Solar System produced the present orbits of the outer planets.

Planetary astrophysical models that assume the planets formed by the accretion of proto–planetary material in their present orbits are beset with great difficulties in explaining the origin of the great quantity of matter far from the Sun that was needed to form Uranus and Neptune and why Uranus is less massive than Neptune .  There are also problems in explaining the origins of the asteroid belt, the Trojan satellites of Jupiter, the irregular satellites of the outer planets, and the formation of the Kuiper Belt beyond Neptune .   Further, the many large craters of the Moon, along with similar evidence of significant cratering on Mercury, Earth, Mars, and the large asteroid Vesta, tell a story of interplanetary violence that occurred about 900 million years after the formation of the Solar System.  Planetary astronomers call this the Late Heavy Bombardment (LHB) period, a succession of collision events that up to now has lacked a plausible explanation.

The orbital dynamics of the Solar System seems deceptively simple.  There is a massive central body, the Sun, and the other objects, being much smaller in mass and widely separated in space, have regular roughly circular orbits that are easily described by applying Newton ’s Laws of gravitation and mechanics.  The Newtonian two-body problem is easily solved, allowing us to understand these orbits.  However, the complications are in the details.  One cannot really neglect the gravitational interactions between the planets, and particularly those between Jupiter and its neighbors.  These interactions perturb planetary orbits and cause them to be unstable over large periods of time.  While one can solve the gravitational two-body problem analytically, the three-body problem, for example involving the Sun and two planets, has no analytic solutions.  When it is solved numerically on a computer, the results are often chaotic, with small differences in starting conditions leading to dramatically different orbital outcomes, including planets ejected from the system.  Thus, the present calm stability of our Solar System is an illusion, with chaos lurking in the past and possibly in the future.

Recently a radical new departure from previous models of Solar System formation, the Nice model, offers to provide an explanation for the mysteries of planet and moon formation and bombardment.  The Nice model is the work of an international team consisting of Alessandro Morbidelli ( France ), Rodney Gomes ( Brazil ), Kleomenis Tsiganis ( Greece ), and Hal Levinson (USA), and is named for the French the city of Nice where their ideas came together.

Basically, the Nice model starts with the four major planets ordered as Jupiter, Saturn, Neptune, and Uranus, with Jupiter in more or less its present orbit and the other planets in concentric orbits with radii increasing outward is steps of about 4.3 AU, with Neptune and Uranus inverted from their present ordering.  In orbit outside Uranus initially are a cloud of thousands of “planetesimals”, icy bodies comparable in mass to the present asteroids but much more numerous.  Roughly speaking, in the Nice model the primitive Solar System looks like a “bull’s eye” target board with four concentric rings (the gas giants) surrounded by a dense outer cloud of dots.

This initial system is somewhat unstable, and as time progresses the major planets interact and alter their orbits a bit, while the outer cloud squeezes together a bit and develops gaps like the Kirkwood zones of the present asteroid belt.  However, despite such movements, nothing much happens for over 800 millions of years, and the system gives the appearance of relative stability.

Then, at about 878 million years after formation of the system, all hell breaks loose.  This occurs because the wanderings of the orbits of Saturn and Jupiter have temporarily come into a 2:1 orbital resonance.  This exerts cumulative forces on the other planets, disrupting the orbits of Neptune and Uranus, and flinging them outward into the cloud of planetesimals, which scatter in all directions.  It takes about another 100 million years for the system to calm down and reach a new state of equilibrium, which is very different from the previous one.

Because Neptune was closer to the Jupiter-Saturn conjunction, its orbit has been disrupted the most, and its orbital radius has increased by about a factor of two.  Uranus has also moved to a larger orbit, which is now inside the orbit of Neptune but further from Saturn than before.  But the biggest effect has been on the outer cloud of planetesimals.  They appear to be gone.  They have has been largely dispersed.  There are a few planetesimals now in stable orbits outside the orbit of Neptune , and these form the present Kuiper Belt.  However, most of them have either collided with the major bodies of the Solar System or have been ejected from the System altogether.  Their disruption has sent many high velocity objects into the inner Solar System, accounting for the Late Heavy Bombardment described above.  Thus, the Nice model explains the Kuiper Belt, the formation of Uranus and Neptune, the low mass of Uranus, the late Heavy Bombardment of the inner planets, and the origins of the Trojans, the irregular moons, and the asteroid belt.

A 7 megabyte QuickTime movie spanning 1.2 billion years of Solar System evolution according to the Nice model has been posted by Sky and Telescope on the Web at http://media.skytonight.com/video/Solar_System_Sim.mov (in this URL, note that there are underscores between Solar, System, and Sim).  The movie has been purposely slowed down at 878 million years so that the violent disruptions of the system, which happen fast, can be viewed more closely.   It’s fun to watch and to try to imagine the planetary violence that must have occurred when the planetesimals start flying off in all directions.

Thus, the Nice model provides a neat explanation of the present configuration and violent past of the Solar System.  It also suggests that, like many other aspects of our present environment, the Solar System is “special”.  When we are able to explore the planetary systems of other stars, we are not likely to find any twins of the Solar System, since its origins are the chaotic result of a particular set of circumstances.  We might, however, find a system like the early Solar System, where a Late Heavy Bombardment is about to begin and the inner planets are about to be subjected to a cosmic 100 million year rock concert.  Space travelers take note.  That would be a system to avoid.

AV Columns Online: Electronic reprints of about 150 "The Alternate View" columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl.washington.edu/av.

References

The Nice Model:

R. Gomes, H. F.Levison, K.Tsiganis, and A.Morbidelli,, Nature 435, 466 (2005).

A. Morbidelli, K. Tsiganis, A. Crida, H. F. Levison, and R. Gomes, Astronomical Journal 134 1790-1798 (2007), arXiv preprint 0706.1713 [astro-ph].