Laskar's Chaos (1989): The Solar System Is Not a Clockwork

Laskar’s 1989 paper showed that the Solar System is chaotic. Following the planets’ orbits over 200 million years, he found that tiny uncertainties grow by a factor of e, about 2.7, every 5 million years, so planetary orbits cannot be predicted beyond about 100 million years.

Is the Solar System stable? The question before 1989

The classical answer came from Laplace and Lagrange. They proved that, to a first approximation in the planets’ masses and in the shapes and tilts of their orbits, the planets move quasi-periodically: their orbits wobble, but in patterns that repeat and never run away. Later astronomers pushed those calculations to higher accuracy. Whether the clockwork really held, over the Solar System’s long life, was still open.

What the paper found

• The motion is chaotic, not quasi-periodic. The classical picture of Laplace and Lagrange breaks down over long timescales.
• A Lyapunov time of about 5 million years. The Lyapunov time measures how fast two almost identical starting states drift apart. Here, small errors in the initial conditions grow by a factor of e every 5 million years.
• A horizon for prediction. Orbits can be predicted over about 10 million years, but not beyond about 100 million years. Over 100 million years an error compounds about 20 times, growing roughly 500 million-fold.
• The inner planets are to blame. The chaos comes mainly from Mercury, Venus, Earth and Mars.
• Chaos is not catastrophe. Laskar stressed that this does not mean Venus and Earth will soon cross orbits, only that standard methods cannot predict such events.

How he did it

Rather than follow each planet around the Sun orbit by orbit, Laskar took a shortcut. In earlier work he had built a large set of averaged, or “secular,” equations for the eight major planets. Averaging smooths out the fast motion of each planet along its orbit and keeps only the slow changes in the orbit’s shape (eccentricity) and tilt (inclination). His equations were accurate to second order in the planetary masses and to fifth order in eccentricity and inclination, and they included corrections from general relativity and the Moon.

He then integrated this system numerically, stepping it backward in time over 200 million years, and watched how nearby solutions diverged.

Why it mattered

Laskar showed that the clockwork Solar System is an illusion on long timescales. Forecasts of the far future had to become statistical: instead of one predicted orbit, astronomers now run many simulations and ask how often something happens. Laskar argued that the qualitative methods pioneered by Poincaré must replace the search for exact solutions.

It also helped replace a static picture with a changing one, a view later extended to the giant planets’ early wanderings in the Nice model of migrating giant planets.

What we know now

Later work by Laskar and Gastineau, in 2009, found that in about 1% of simulated futures Mercury’s orbit becomes unstable within the Sun’s lifetime. That figure is a key input to forecasts of when the Sun will die and what happens to the planets, alongside models of the Sun’s red giant future.

The outer planets look far steadier on their own, but even they have limits. A 2026 study accepted for The Astrophysical Journal Letters found that uneven mass loss from the dying Sun could break up the outer Solar System roughly a billion years after it becomes a white dwarf.

Who wrote it

J. Laskar was the sole author. The Nature paper is just two pages long, built on the secular equations he had constructed in earlier papers. Semantic Scholar lists about 417 citations (October 2026).

Read the original

Laskar, J. (1989). “A numerical experiment on the chaotic behaviour of the Solar System.” Nature 338, 237-238. doi:10.1038/338237a0

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