Stability of the Solar System
Though the planets have historically been stable as observed, and will be in the "short" term, their weak gravitational effects on one another can add up in ways that are not predictable by any simple means.
For this reason (among others), the Solar System is chaotic in the technical sense defined by mathematical chaos theory,[1] and that chaotic behavior degrades even the most precise long-term numerical or analytic models for the orbital motion in the Solar System, so they cannot be valid beyond more than a few tens of millions of years into the past or future – about 1% its present age.
[4] Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, V. Arnold, and J. Moser) have searched for evidence for the stability of the planetary motions, and this quest has led to many mathematical developments and several successive "proofs" of stability of the Solar System.
Modeling the Solar System is a case of the n-body problem of physics, which is generally unsolvable except by numerical simulation.
At one point, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course, with 1–2% probability, 3–4 billion years into the future.
This 8:4:2:1 resonance will cause Callisto to migrate outward, and it may remain stable with approximately 56% probability, or become disrupted with Io usually exiting the chain.
[19] In 2022, Garett Brown and Hanno Rein of the University of Toronto published a study exploring the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys.
[20] Project LonGStOP (LOng-term Gravitational Study of the Outer Planets) was a 1982 international consortium of Solar System dynamicists led by A.E.
Its results revealed several curious exchanges of energy between the outer planets, but no signs of gross instability.
In 1988, Sussman and Wisdom found data using the Orrery that revealed that Pluto's orbit shows signs of chaos, due in part to its peculiar resonance with Neptune.
This might be more than a technicality, since even a Solar System body as small as Pluto might affect the others to a perceptible extent through cumulative gravitational perturbations.
[22] 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.
[13] Independently of Laskar and Gastineau, Batygin and Laughlin were also directly simulating the Solar System 20 billion years into the future.
[b] Their results reached the same basic conclusions as did Laskar and Gastineau, while additionally providing a lower bound of a billion years on the dynamical lifespan of the Solar System.
[24] In 2020, Garett Brown and Hanno Rein of the University of Toronto published the results of their numerical integration of the Solar System over 5 billion years.
