Stability of the Solar System


Stability of the Solar System

The stability of the Solar System is a subject of much inquiry in astronomy. The Solar System is chaotic,cite journal
title=Large-scale chaos in the solar system
author=J. Laskar
journal=Astronomy and Astrophysics
volume=287
pages=L9–L12
year=1994
url=http://adsabs.harvard.edu/abs/1994A%26A...287L...9L
] though by most predictions it is stable in that none of the planets will collide with each other or be ejected from the system in the next few billion years, and the Earth's orbit will be relatively stable. [Gribbon,John. Deep Simplicity. Random House 2004.]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability for the solar system. [Laskar, J. Solar System: Stability [http://adsabs.harvard.edu/abs/2000eaa..bookE2198L] ]

Overview and challenges

The orbits of the planets are open to long-term variations, and modeling the solar system is subject to the n-body problem.

One notable example of the chaos in the solar system is the Neptune-Pluto system, which lies in a 3:2 orbital resonance. Although the resonance itself will remain stable, it becomes impossible to predict the position of Pluto with any degree of accuracy more than 10–20 million years (the Lyapunov time) into the future.cite journal | title = Numerical evidence that the motion of Pluto is chaotic | author = Gerald Jay Sussman, Jack Wisdom | journal = Science | volume = 241 | pages = 433–437 | year = 1988 | url = http://adsabs.harvard.edu/abs/1988Sci...241..433S | doi = 10.1126/science.241.4864.433] Another example is Earth's axial tilt which, thanks to friction raised within Earth's mantle by tidal interactions with the Moon (see below), will be rendered chaotic at some point between 1.5 and 4.5 billion years from now. [cite journal|title=On the long term evolution of the spin of the Earth|author=O. Neron de Surgy, J. Laskar|journal=Astronomy and Astrophysics|date=February 1997|volume=318|pages=975–989|url=http://adsabs.harvard.edu/abs/1997A%26A...318..975N|accessdate=2008-06-08]

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.cite journal | author=Wayne B. Hayes | title=Is the outer Solar System chaotic? | journal=Nature Physics | id=arXiv|astro-ph|0702179 | year=2007 | volume=3 | pages=689–691 | doi=10.1038/nphys728 | url=http://adsabs.harvard.edu/abs/2007NatPh...3..689H] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical. [cite book
author=Ian Stewart
title=Does God Play Dice?
publisher=Penguin Books
edition=2nd
pages=246–249
year=1997
isbn=0-14-025602-4
]

Ultimately, the Solar System is stable in that none of the planets will collide with each other or be ejected from the system in the next few billion years. Beyond this, within five billion years or so Mars's eccentricity may grow to around 0.2, such that it lies on an Earth-crossing orbit, leading to a potential collision. In the same timescale, Mercury's eccentricity may grow even further, and a close encounter with Venus could theoretically eject it from the Solar System altogether or send it on a collision course with Venus or Earth. [cite news|title=The solar system could go haywire before the sun dies|url=http://space.newscientist.com/article/dn13757-solar-system-could-go-haywire-before-the-sun-dies.html?feedId=online-news_rss20 | author=David Shiga | work=NewScientist.com News Service | date=23 April 2008 | accessdate=2008-04-28]

In calculation, the unknowns include asteroids, the solar quadruple moment mass loss from the Sun through radiation and solar wind, and drag of solar wind on planetary magnetospheres, galactic tidal forces, the fractional effect, and effects from passing stars. [The stability of the solar system. http://physics.technion.ac.il/~litp/dist/dist_presentations/technion1.ppt.] Furthermore, the equations of motion describe a process that is inherently serial, so there is little gain from massively parallel computers.

tudies

Longstep

[http://adsabs.harvard.edu/abs/1988VA.....32...95R Project LONGSTOP] (Long-term Gravitational Study of the Outer Planets) was a 1982 international consortium of Solar System dynamicists led by Archie Roy. It involved creation of a model on supercomputer, integrating the orbits of (only) the outer planets. Its results revealed several curious exchanges of energy between the outer planets, but no signs of gross instability .

Digital Orrery

Another project involved constructing the Digital Orrery by Gerry Sussman and his MIT group in 1988. The group used a supercomputer to integrate the orbits of the outer planets over 845 million years (some 20 per cent of the age of the Solar System). In 1988, Sussman and Wisdom found data using the Orrery which revealed that Pluto's orbit shows signs of chaos, due in part to its peculiar resonance with Neptune.

If Pluto's orbit is chaotic, then technically the whole Solar System is chaotic, because each planet, even one as small as Pluto, affects the others to some extent through gravitational interactions. [ [http://www.fortunecity.com/emachines/e11/86/solarsys.html Is the Solar System Stable? ] ]

Laskar

In 1989, Jacques Laskar of the Bureau des Longitudes in Paris published the results of his numerical integration of the Solar System over 200 million years. These were not the full equations of motion, but rather averaged equations along the lines of those used by Laplace. Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time.

References


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