- Stability of the Solar System
The

**stability of the Solar System**is a subject of much inquiry inastronomy . TheSolar 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 theEarth '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 andJürgen 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 3:2orbital 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 (theLyapunov 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'saxial tilt which, thanks to friction raised within Earth's mantle by tidal interactions with theMoon (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=0-14-025602-4Ultimately, 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 withVenus 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=2008-04-28In calculation, the unknowns include

asteroid s, thesolar quadruple moment mass loss from theSun through radiation andsolar wind , and drag of solar wind on planetarymagnetosphere s, galactictidal forces , thefractional effect , and effects from passingstar s. [*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 inherentlyserial , so there is little gain frommassively parallel computer s.**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 byArchie 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 peculiarresonance withNeptune .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 theBureau 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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