**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 that Earth's orbit will be relatively stable.

What keeps our solar system stable?

So what are the results? Most of the calculations agree that eight billion years from now,

**just before the Sun swallows the inner planets and incinerates the outer ones, all of the planets will still be in orbits very similar to their present ones**. In this limited sense, the solar system is stable.

https://www.ias.edu/ideas/2011/tremaine-solar-system
**Is the Solar System Stable?**
The stability of the

solar system is one of the oldest problems in theoretical physics, dating back to

Isaac Newton. After Newton discovered his famous laws of motion and gravity, he used these to determine the motion of a single planet around the Sun and showed that the planet followed an ellipse with the Sun at one focus. However, the actual solar system contains eight planets, six of which were known to Newton, and each planet exerts small, periodically varying, gravitational forces on all the others.

The puzzle posed by Newton is whether the net effect of these periodic forces on the

planetary orbits averages to zero over long times, so that the planets continue to follow orbits similar to the ones they have today, or whether these small mutual interactions gradually degrade the regular arrangement of the orbits in the solar system, leading eventually to a collision between two planets, the ejection of a planet to interstellar space, or perhaps the incineration of a planet by the Sun. The interplanetary gravitational interactions are very small—the force on Earth from Jupiter, the largest planet, is only about ten parts per million of the force from the Sun—but the time available for their effects to accumulate is even longer: over four billion years since the solar system was formed, and almost eight billion years until the death of the Sun.

Newton’s comment on this problem is worth quoting: “the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted, which may have arisen from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation.” Evidently Newton believed that the solar system was unstable, and that occasional divine intervention was required to restore the well-spaced, nearly circular planetary orbits that we observe today. According to the historian

Michael Hoskin, in Newton’s world view “God demonstrated his continuing concern for his clockwork universe by entering into what we might describe as a permanent servicing contract” for the solar system.

Other mathematicians have also been seduced into philosophical speculation by the problem of the stability of the solar system. Quoting Hoskin again, Newton’s contemporary and rival

Gottfried Leibniz “sneer[ed] at Newton’s conception, as being that of a God so incompetent as to be reduced to miracles in order to rescue his machinery from collapse.” A century later, the mathematician

Pierre Simon Laplace was inspired by the success of

celestial mechanics to make the famous comment that now encapsulates the concept of causal or

Laplacian determinism: “An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.”

Many illustrious mathematicians and physicists have worked on this problem in the three centuries since Newton, including Vladimir Arnold, Boris Delaunay, Carl Friedrich Gauss, Andrei Kolmogorov, Joseph Lagrange, Laplace, Jürgen Moser,

Henri Poincaré, Siméon Poisson, and others. Several “proofs” of stability have been announced in the course of these labors; these have all been based on approximations that are not completely accurate for our own solar system and thus do not prove its stability. Nevertheless, research on this problem has led to many new mathematical tools and insights (perturbation theory, the KAM theorem,etc.) and inspired the modern disciplines of nonlinear dynamics and chaos theory.

The long-term behavior of the solar system is also relevant to a variety of other issues. Particle accelerators such as the

Large Hadron Collider must guide protons for over a hundred million orbits, a problem similar in several respects to maintaining the planets on stable orbits for the lifetime of the solar system. The delivery of

meteorites to Earth from their birthplace in the asteroid belt is driven by the long-term evolution of asteroid orbits due to forces from Jupiter and other planets. The primary mechanism that drives

climate change and ice ages on timescales of tens of thousands of years is the periodic variation in the Earth’s orbit due to forces from the other planets. The discovery of hundreds of extrasolar planetary systems in the last two decades raises the tantalizing possibility that some or all of their properties are determined by the requirement that these systems have been stable for billions of years. In a different arena, some astronomers argue that

Robert Frost’s famous poem “Fire and Ice” was inspired by the possible fates of the Earth at the demise of the solar system.

The most straightforward way to solve the problem of the stability of the solar system is to follow the planetary orbits for a few billion years on a computer. All of the

planetary masses and their present orbits are known very accurately and the forces from other bodies—passing stars, the Galactic tidal field, comets, asteroids, planetary satellites, etc.—are either easy to incorporate or extremely small. There are two main challenges. The first is to devise numerical methods that can follow the motions of the planets with sufficient accuracy over a few billion orbits; this was solved by the development in the 1990s of symplectic integration algorithms, which preserve the geometrical structure of dynamical flows in multidimensional phase space and thereby provide much better long-term performance than general-purpose integrators.The second challenge was the overall processing time needed to follow planetary orbits for billions of years; this was solved by the exponential growth in speed of computing hardware that has persisted for the last five decades. At the present time, following planetary systems over billion-year intervals is difficult mostly because it is a

*serial* problem—you have to follow the orbits from 2011 to 2020 before you can follow them from 2021 to 2030—whereas most of the computational speed gains of the last few years have been achieved by parallelization, the distributing of a computing problem among hundreds or thousands of processors that work simultaneously.