Three-body tango

Let’s start a new section in physics napkins, called scitoys, for scientific toys. The idea goes as follows: I write down code to illustrate something in physics or maths in an animation. The animation is displayed here, with some explanations and some ideas about further development… So, if you’re a jedi master, you can enjoy the challenges…

This first scitoy is just a running test… the ones I’m preparing are more spectacular. So, in three-body tango, we show three particles interacting through gravitational attraction. I’m pretty sure you all know by now that the two-body gravitational interaction (in Newtonian mechanics) is as regular as a cuckoo clock, while the intrusion of a third body makes it chaotic. You can see in the video how the planets change couple in a chaotic way…

Some technicalities… the program is in C++ for linux with X11. I will send the code to anyone interested and, in due time, I will publish it for all the scitoys. The video capture was done with xvidcap.

A technicality related to this particular program: the gravitational interaction has a short-distance cutoff. I mean: if the planets come closer than a certain minimal distance, I don’t allow the force to accumulate anymore. This avoids some instabilities…

And the challenge: how many perfectly periodic orbits can you find? Are they stable?

With a wink for Miguel Ibáñez Berganza & Daniel Gómez Lendínez

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