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In 2009, two researchers ran a simple [br]experiment.

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They took everything we know about our[br]solar system and calculated

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where every planet would be up to 5 [br]billion years in the future.

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To do so they ran over 2000 numerical [br]simulations

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with the same exact initial conditions[br]except for one difference:

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the distance between Mercury and the Sun,[br]modified by less than a millimeter

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from one simulation to the next.

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Shockingly, in about 1 percent of their [br]simulations,

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Mercury’s orbit changed so drastically [br]that it could plunge into the Sun

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or collide with Venus.

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Worse yet,

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in one simulation it destabilized[br]the entire inner solar system.

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This was no error; the astonishing variety[br]in results

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reveals the truth that our solar system [br]may be much less stable than it seems.

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Astrophysicists refer to this astonishing[br]property of gravitational systems

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as the n-body problem.

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While we have equations that can [br]completely predict the motions

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of two gravitating masses,

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our analytical tools fall short when [br]faced with more populated systems.

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It’s actually impossible to write down[br]all the terms of a general formula

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that can exactly describe the motion[br]of three or more gravitating objects.

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Why? The issue lies in how many unknown[br]variables an n-body system contains.

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Thanks to Isaac Newton, we can write [br]a set of equations

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to describe the gravitational force [br]acting between bodies.

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However, when trying to find a general [br]solution for the unknown variables

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in these equations,

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we’re faced with a mathematical [br]constraint: for each unknown,

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there must be at least one equation [br]that independently describes it.

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Initially, a two-body system appears to[br]have more unknown variables

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for position and velocity than [br]equations of motion.

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However, there’s a trick:

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consider the relative position and [br]velocity of the two bodies

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with respect to the center of [br]gravity of the system.

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This reduces the number of unknowns[br]and leaves us with a solvable system.

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With three or more orbiting objects in the[br]picture, everything gets messier.

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Even with the same mathematical trick [br]of considering relative motions,

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we’re left with more unknowns than [br]equations describing them.

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There are simply too many variables[br]for this system of equations

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to be untangled into a general solution.

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But what does it actually look like for [br]objects in our universe

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to move according to analytically [br]unsolvable equations of motion?

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A system of three stars––

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like Alpha Centauri could come crashing[br]into one another or, more likely,

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some might get flung out of orbit [br]after a long time of apparent stability.

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Other than a few highly improbable [br]stable configurations,

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almost every possible case is [br]unpredictable on long timescales.

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Each has an astronomically large range[br]of potential outcomes,

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dependent on the tiniest of differences[br]in position and velocity.

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This behaviour is known as chaotic [br]by physicists,

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and is an important characteristic [br]of n-body systems.

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Such a system is still deterministic—[br]meaning there’s nothing random about it.

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If multiple systems start from the exact[br]same conditions,

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they’ll always reach the same result.

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But give one a little shove at the start,[br]and all bets are off.

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That’s clearly relevant for human space[br]missions,

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when complicated orbits need to [br]be calculated with great precision.

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Thankfully, continuous advancements[br]in computer simulations

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offer a number of ways[br]to avoid catastrophe.

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By approximating the solutions with [br]increasingly powerful processors,

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we can more confidently predict the motion[br]of n-body systems on long time-scales.

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And if one body in a group of three is so[br]light it exerts no significant force on the other two,

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the system behaves, with very good [br]approximation, as a two-body system.

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This approach is known as the “restricted [br]three-body problem.”

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It proves extremely useful in describing,[br]for example,

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an asteroid in the Earth-Sun [br]gravitational field,

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or a small planet in the field of a [br]black hole and a star.

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As for our solar system, you’ll [br]be happy to hear

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that we can have reasonable confidence[br]in its stability

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for at least the next several [br]hundred million years.

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Though if another star, launched from [br]across the galaxy, is on its way to us,

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all bets are off.