Stability of the Solar System

The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways.For this reason (among others) the Solar System is chaotic in the technical sense of mathematical chaos theory, and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years. The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways.For this reason (among others) the Solar System is chaotic in the technical sense of mathematical chaos theory, and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years. The Solar System is stable in human terms, and far beyond, given that it is unlikely any 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. 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 of the Solar System. The orbits of the planets are open to long-term variations. Modeling the Solar System is a case of the n-body problem of physics, which is generally unsolvable except by numerical simulation. Orbital resonance happens when any two periods have a simple numerical ratio. The most fundamental period for an object in the Solar System is its orbital period, and orbital resonances pervade the Solar System. In 1867, the American astronomer Daniel Kirkwood noticed that asteroids in the asteroid belt are not randomly distributed. There were distinct gaps in the belt at locations that corresponded to resonances with Jupiter. For example, there were no asteroids at the 3:1 resonance – a distance of 2.5 AU – or at the 2:1 resonance at 3.3 AU (AU is the astronomical unit, or essentially the distance from the Sun to Earth). These are now known as the Kirkwood gaps. Some asteroids were later discovered to orbit in these gaps, but their orbits are unstable and they will eventually break out of the resonance due to close encounters with a major planet. Another common form of resonance in the Solar System is spin–orbit resonance, where the period of spin (the time it takes the planet or moon to rotate once about its axis) has a simple numerical relationship with its orbital period. An example is our own Moon, which is in a 1:1 spin–orbit resonance that keeps the far side of the Moon away from the Earth. Mercury is in a 3:2 spin–orbit resonance. The planets' orbits are chaotic over longer timescales, in such a way that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years. 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. In calculation, the unknowns include asteroids, the solar quadrupole moment, mass loss from the Sun through radiation and solar wind, drag of solar wind on planetary magnetospheres, galactic tidal forces, and effects from passing stars. Furthermore, the equations of motion describe a process that is inherently serial, so there is little to be gained from using massively parallel computers.