How would three stars orbit each other? This is an old problem in celestial mechanics called the three-body problem that turns out to be tremendously difficult. We have solutions for some very special cases. This gif illustrates a few of them.
http://likeaphysicist.tumblr.com/post/54182255663/mathology-twocubes-some-time-ago-a
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Join mathematicians Dana Ernst , Sara Del Valle , Vincent Knight , Luis Guzman and Robert Jacobson as they talk with Amy Robinson about their favorite math gifs and ideas and what it’s like to be a mathematician. How many numbers are there? Do mathematicians see the world differently? And why is the last panel of this xkcd comic funny? http://xkcd.com/804/
Dana Ernst is an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ, USA.
Sara Del Valle is a mathematical epidemiologist at Los Alamos National Laboratory in Los Alamos, NM, USA.
Vincent Knight is a LANCS lecturer at the Cardiff University School of Mathematics in Operational Research in Cardiff, Wales, UK.
Luis Guzman is a graduate student in mathematics at the University of West Florida in FL, USA.
Robert Jacobson is Assistant Professor of Mathematics at Roger Williams University in RI, USA.
Hangout hosted by Science on Google+’s Amy Robinson
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Ian James – the Earth, Moon, and Sun constitute a version of the three body problem that has some non-trivial applications for us humans.
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Ian James : The problem is classically referred to as the “three body problem”, and I think the earth-moon-sun is widely considered the earliest example. I don’t think there’s a formulation that requires each body to be either an “orbiter” or an “orbited” object; three suns is just one formulation of the problem, and in fact the mathematics are somewhat more interesting when the three bodies are not the same mass and size, so planets, comets, stars, black holes can all form these systems. But the math is similar and related, and definitely can be used to model the earth-moon-sun interactions.
Still, we have found actual trinary star systems, if you want a more direct example — there are even systems with six or seven stars that may interact with one another gravitationally… that would be some fun math to play with… All of this may be a good topic for the hangout, too!
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Ian James those fancy animated gifs are a subset of the problem. The three body problem is much more encompassing than the few solutions shown in this post. Furthermore, as I understand it, the three body problem doesn’t really care about “x orbits y”, just that there is gravitational interaction between the bodies (and this is what determines who orbits what and how, not the other way around).
Consider the Sun, Earth and Moon (which is the first widely studied three body problem). It is three body because there are three objects with mass and velocity. If we freeze the system in place right now and and use the actual positions, velocities, masses, etc of the bodies, we should find a solution in which the Moon orbits the Earth which orbits the Sun. If however, you were to change the initial velocities of the bodies, you might find a different solution.
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Ian James http://en.wikipedia.org/wiki/N-body_problem
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Oh, yeah, we definitely go looking for problems.; that doesn’t mean they’re not applicable, but a lot of math is done for fun or love of the game (google Fermat, Poincare, or Riemann). You’re right that the solar system is more than a 3-body problem, in a pure math sense. The problem is, if we can’t solve the 3-body problem, we can’t solve for higher numbers, so mathematicians tend to start at the next-hardest-problem. Right now that’s 3-body. If someone could solve an arbitrary n-body problem that’d be great, but noone expects that (for now).
I’m sure there are parallels in biology. We break down bodily functions into smaller and smaller pieces to determine how things work separately hoping that what we uncover will help explain how entire systems work. There are people focused on DNA, genes, particular diseases, individual systems, different types of animals, and a thousand other things. Discoveries in one area, even accidental ones, have a history of changing the field. Asking why we don’t just try to solve a 15-body problem instead of the 3-body is like asking why we don’t just try to cure cancer and stop fussing with genes and cells and proteins.
Math works the same way… when people started studying prime numbers, I doubt they could have predicted their value towards computational encryption, and the advances that area have pushed to computation in general. But primes pose a fun, challenging math problem, and we’ve been whittling away at them for centuries, and gaining a lot for it. Same goes for the n-body problem — how the stars and planets move has been a question since before Galileo, and like the work he did, finding equations to explain the 3-body problem are a stepping stone with a rich history and lots of reasons to believe that solving this step will open up more, and more interesting, problems in the next step, and the step after that… and who knows what else will be affected by the work done on the way? Maybe this math will save us all from colliding with Pluto some day (in the rather distant future). You’ll thank us then!
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