How Chaotic Is the Solar System?

by Carson
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An illustration of the Sun and the planets, along with some asteroids and comets

The Solar System seems orderly at first glance. You’ve got the Sun and the eight planets in their own places, and there are some asteroids safely between Mars and Jupiter. But in reality, the Solar System is chaotic. It behaves unpredictably over timescales of billions of years. But how could this happen? Let’s learn about the chaos of the Solar System in this article.

The N-body Problem

Before we explore the chaos of the Solar System, let’s first learn about the n-body problem. It is a problem that aims to describe the motions of multiple gravitationally interacting bodies. It might seem simple to you at first. The gravitational forces between two objects are directly proportional to their total mass and inversely proportional to their distance. Also, the two-body problem is entirely solvable, and the motions between the two objects might look simple. But when you extend it to three bodies, it starts becoming chaotic.

While the two-body problem has definite solutions, N-body problems where N>2 do not. Since there are no known analytical solutions to these problems, we need to solve them numerically. Although they are not exact, these methods are highly accurate when predicting the positions of celestial objects such that we can aim space probes at them.

Why Is Our Solar System Chaotic?

So if we can conduct spaceflight with precision in the Solar System, why would we say it’s chaotic? Well, it’s very stable and predictable in human timescales, but positions start to become impossible to calculate if we’re talking about timescales of millions or billions of years.

That’s because a system like this is very sensitive to its initial conditions. When many parts interact with each other, even a slight change in one of the parameters could result in the objects acting entirely differently in the long run. The longer the simulation goes, the larger the discrepancy becomes from the predicted values.

Take an asteroid on a close approach to Jupiter, for example. The planet’s powerful gravity could get the asteroid anywhere, from sending it to a comet-like orbit approaching the inner planets, to ejecting it out of the Solar System altogether. All of this depends on the distance and angle at which it approaches the giant planet. These parameters could be highly uncertain, especially if it’s approaching close to the planet. This could change the orbit by a significant amount, as gravity assists essentially amplify measurement uncertainties. The asteroid could be predicted to be ejected, but instead, it could be on an Earth-bound trajectory!

The orbit of 81P/Wild 2 from 1920 to 1985 projected on the plane of the ecliptic, showing how it changed due to a close approach of Jupiter.
Note that 81P did not have a hyperbolic orbit to begin with, but its closed orbit before the Jupiter approach was so large that the graph could not plot its entirety without risking losing details on the post-approach orbit.
Data source: JPL Horizons
Blue: Earth; Red: Mars; Brown: Jupiter; Magenta; 81P/Wild 2; Yellow: Saturn

Powered by close approaches and other gravitational interactions such as orbital resonances, the Solar System is chaotic over long timescales. But still, researchers can study the solar system’s evolution and even predict the orbits of dynamically unstable objects. How is it done?

The Method of Statistical Analysis

Researchers use statistical analysis to do numerical integrations on chaotic systems like this. We don’t make the measurements as precise as possible. As long as it’s a measurement, there are inevitably errors that will affect the end state drastically. Instead, we make many clones of the simulation and change the parameters based on the uncertainties of the measurements. Then, we run all the simulations, analyze their end states, and derive statistical information from them.

For such a chaotic system like the Solar System, where many close approaches can affect things a lot, we don’t use standard deviations to obtain the uncertainties of the results. Instead, we split the results into scenarios and obtain the probabilities of each case. This is done by counting how many simulations end up in this state, divided by the number of total simulations in the research.

In fact, this method is not limited to getting data about our Solar System. It can also be used to study other dynamical systems, like predicting the weather based on the current conditions of the atmosphere.

How Chaotic is the Solar System?

After introducing the chaotic nature of the Solar System, some of you might have one question remaining in your heads — just how chaotic is our Solar System? Well, it’s very chaotic in timescales of billions of years, even before the Sun reaches its red giant phase and swallows the inner planets. You could expect any behavior from such a system if you repeat the configuration enough.

This is spectacularly demonstrated in a study by Laskar and Gastineau (2009). The researchers simulated 2501 slightly different Solar Systems, whose slight differences are within measurement uncertainties. They found that in 20 cases, Mercury’s eccentricity increased to above 0.9, allowing collisions between the Sun or the inner planets. In fact, a few of those collisions have already been logged on the research paper. One simulation even showed a very close approach between Earth and Mars!

Even more spectacularly, the orbits of asteroids and comets are even more unpredictable. Some of them are on planet-crossing orbits, where close approaches can easily change the orbits of the objects. Moreover, smaller asteroids are influenced by sunlight. Depending on its shape and rotation, the Yarkovsky effect can exert a small force on the asteroid over time, further complicating the prediction of the consequences of close approaches. Even worse, comets experience asymmetric outgassing, which change their trajectories in chaotic ways. Although those small objects might not play a significant role in the evolution of the orbits of planets, it is at the center of planetary defense, where asteroids are tracked, and impacts are identified, predicted, and prevented.

Conclusion

To conclude, the Solar System is chaotic. Even if we have measured the positions of the planets very accurately, the N-body nature of the system means that it is so unpredictable that we need to use statistical methods when researching it at long timescales. If you would like to include something that we have not, please leave the points in the comments below.

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