The solar system will be stable for at least the next 100,000 years

The solar system will be stable for at least the next 100,000 years

The semi-major axis of a planetary orbit. Credit: Sndeep81, Wikimedia Commons

It’s nice to have a feel-good story every now and then, so here’s one to stave off the existential dread: Earth probably won’t be ejected into deep space for at least 100,000 years. In fact, all the planets of the solar system are safe for that time frame, so there’s good news everywhere for you and your favorite planetary body.

It might be worth backing up a bit. The chances of Earth, or any planet for that matter, being knocked out of orbit are always slim. As Newtonian physics tells us, a moving object stays in motion unless some other force acts on it — and for something the size of a planet it would take a significant force to push a planet off track. But there are examples of planetary realignment in the solar system’s own history. One of the most widely accepted models of solar system formation, the Nice model, describes how the outer planets migrated early in the solar system’s history and are said to have wreaked havoc on the inner rocky worlds, possibly displacing or even swallowing smaller protoplanets.

But now researchers have done the math to show that such a migration is unlikely in the next 100,000 years. Angel Zhivkov and Ivaylo Tounchev of the Department of Mathematics and Computer Science at Sofia University in Bulgaria used computer calculations to determine that the planets are likely to remain stable. Their eccentricities (how much their orbit is different from circular) will remain small, as will their inclination (how far above or below the plane of the solar system they travel). Likewise, the semimajor axes (the radius of the longest part of an elliptical orbit) will not change significantly for any of the planets.

A simulation of all known near-Earth objects from January 2018. The solar system is a busy place – luckily most objects are small, with a lot of empty space separating them from us and each other. Credit: NASA/JPL-Caltech.

Even the degraded dwarf planet Pluto was included in this study, and diehard Pluto fans will be happy to know that it too will likely do little more than oscillate a little over the next 100,000 years.

So what happens after 100,000 years? The further you go in time, the more difficult predictions become, because the real universe is always a bit chaotic, but Zhivkov and Tounchev believe that “with simple additional reasoning and evaluations … the theorem can be proven a million years ago.” In that time frame, there probably won’t be any problems either. And if you’re really concerned, it just takes some extra computing power that the researchers couldn’t harness, and “the stability of the solar system could be proven in the next five billion years,” they say.

Of course the model is not perfect. It does not take into account relativistic effects, and the math assumes that the planets are point masses, which, of course, they are not in real life. But perhaps the most glaring omission in the calculation is the millions of smaller bodies in the solar system: asteroids, comets, and everything in between. By themselves, the gravitational effects of these objects are negligible, but as a collective they can certainly planets a bit around. To include them all in the model would be a monumental task, and one with diminishing returns. It’s not something that should keep you up at night.

So Earthlings, Martians and Jovians alike, take a deep breath and enjoy the ride. The next 100,000 years around the sun will run smoothly.

More information:
Angel Zhivkov et al, A Computer Aided Evidence for 100,000 Years of Solar System Stability, arXiv (2022). arXiv:2206.13467 [astro-ph.EP]

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