One of the most curious unsolved problems in physics is the three-body problem, which despite its name is not about a ménage-à-trois. It has to do with calculating the trajectory of orbits of three (or more) objects around a common center of mass, and despite many years of study, the equations it generates seem to have no general solution.
There are specific solutions for objects of a particular mass starting out with a particular set of coordinates and velocities, and lots of them result in highly unstable orbits. But despite the fact that there are computer models that can predict the movements of three objects in a gravitational dance -- such as the members of a triple-star system -- the overarching mathematical framework has proven intractable.
How, then, can we predict the orbits of the eight planets (and countless dwarf planets, asteroids, and comets) around the Sun to such high precision? Some of the great names of physics and astronomy in the sixteenth and seventeenth centuries -- Galileo Galilei, Tycho Brahe, Johannes Kepler, and Isaac Newton, especially -- used highly accurate data on planetary positions to conclude that the planets in the Solar System go around the Sun in elliptical orbits, all powered by the Universal Law of Gravitation. The mathematical model they came up with worked to a high degree of accuracy, allowing earthbound astronomers to predict where the planets were in the sky, and also such phenomena as eclipses.
The reason it works, and doesn't fall prey to the three-body problem chaos, is that the Sun is so massive in comparison to the objects orbiting it. Because the Sun is huge -- it has a thousand times more mass than the largest planet, Jupiter -- its gravitational pull is big enough that it swamps the pull the planets exert on each other. For most purposes, you can treat each orbit as independent two-body problems; you can (for example) look at the masses, velocities, and distances between the Sun and Saturn and ignore everything else for the time being. (Interestingly, it's the slight deviation of the orbit of Uranus from the predictions of its position using the two-body solution that led astronomers to deduce that there must be another massive planet out there pulling on it -- and in 1846 Neptune was observed for the first time, right where the deviations suggested it would be.)
I said it was "lucky" that the mass imbalance is so large, but I haven't told you how lucky. It turns out that all you have to do is add one more object of close to the same size, and you now have the three-body problem, and the resulting orbit becomes unpredictable, chaotic, and -- very likely -- unstable.
It's what I always think about when I hear woo-woos burbling on about Nibiru, a huge extrasolar planet that has been (repeatedly) predicted to come zooming through the Solar System. We better hope like hell this doesn't happen, and not because there could be collisions. A huge additional mass coming near the Earth would destabilize the Earth's orbit, and could cause it to change -- very likely making it more elliptical (meaning we'd get fried at perigee and frozen at apogee). Interestingly, this is one thing that even the writers of Lost in Space got right, at least temporarily. The planet John Robinson et al. were on had a highly elliptical orbit, leading to wild climatic fluctuations. The "temporarily" part, though, came about because apparently the writers found it inconvenient to have the Robinson Family deal with the alternating icebox/oven climate, and after a short but dramatic story arc where they were contending with it, it never happened again.
Or maybe the planet just decided to settle down and behave. I dunno.
This does bring up an interesting question, though; if they're out in outer space, but emit no light, how do we know they're there? Well, they were conjectured for decades, based on the argument above, about orbital instability; but as far as detection goes, that's proven harder. But now, we have actually detected one, and how we did it is absolutely staggering.
One of the outcomes of Einstein's General Theory of Relativity is that the presence of matter warps space. A common two-dimensional analogy is a bowling ball sitting on a trampoline, deflecting the membrane downward. If you roll a marble on the trampoline, it'll curve around the bowling ball, not because the bowling ball is magically attracting the marble, but because its presence has changed the shape of the space the marble is moving through. Scale that up by one dimension, and you've got the idea.
What's cool about this is that because it's the shape of spacetime that has warped, everything passing through that region is affected -- including light. This is called gravitational lensing, and has been used to infer the positions and masses of black holes, which (duh) are black and therefore hard to see. But by detecting the distortion of light emitted by objects behind the black hole, we can see its effects.
And now, that's been done with a rogue exoplanet. Judging by the lensing effect it created, it's about the mass of Saturn, and the conclusion based on its mass and velocity was that it was indeed once part of a planetary system -- and then got ejected, probably because of a close encounter with another massive object, or perhaps because it was part of a multiple star system and was in an unstable orbit from the get-go.
Now, though, it's lost -- a lonely wanderer tracking its way through the vastness of interstellar space. How many of these rogue planets there are is unknown; as you probably concluded, detection isn't easy, relying on having a powerful telescope aimed in the right direction at the moment the planet passes in front of a distant star. But given how easy it is to destabilize an orbit, there are likely to be millions.
Which, we have to hope, will all stay the hell away from us. Nibiru notwithstanding, having a rogue planet pass through the Solar System would make even Donald Trump drop to number two on the List Of The Biggest Current Threats To Humanity. Fortunately, it's unlikely; space is big. We'd also likely have a decent amount of warning, because as soon as it got near enough (right around the orbit of Pluto), it'd reflect enough of the Sun's light that it'd become visible to astronomers.
Unfortunately, though, there's probably nothing much we could do about it. We've just begun to experiment with the possibility of deflecting small asteroids; deflecting an entire planet, especially one the size of Saturn, would be a case where the best strategy would be to stick your head between your legs and kiss your ass goodbye.
I mean, not to end on a pessimistic note. Let's all focus on the "unlikely" part. And continue working on the next biggest threat, which frankly is occupying more of my anxiety at the moment.
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