Figure Eight Orbit
June 1st, 2005 by WaltThe three body problem in physics is the study of the trajectories of three bodies mutually attracted by (Newtonian) gravity. Unlike the two body problem, the three body problem cannot be solved in general, but some specific solutions are known. An article in the Notices of the AMS reports that a new (well, new circa 2001) solution has been found where all three bodies travel in the same orbit — a figure eight.
The figure eight orbit is stable, which means that it is robust under small perturbations. Since any actual physical system will be perturbed slightly by the gravitational pull of other bodies, stability is a prerequisite for a solution to actually be found in nature. So the figure eight orbit may someday be observed by astronomers.
June 2nd, 2005 at 12:24 pm
Unfortunately “numerical experiments done by Douglas Heggie suggest that the probability of an eight is somewhere between one per galaxy and one per universe.”
June 2nd, 2005 at 1:51 pm
Then the sole purpose of NASA should be to build one of these somewhere beyond the orbit of Pluto.
June 2nd, 2005 at 4:45 pm
ROTFLMAO
In my opinion, there has never been a more quintessential “Walt” statement in the history of the universe. Nineteen words that perfectly encapsulate your essense. I am stunned by their perfection. Speechless. But of course, I can still type.
June 2nd, 2005 at 6:52 pm
Is it stable enough that you could use one of the Lagrange points (e.g. L4 or L5) of the earth-moon orbit?
That might be more within NASA’s reach and would be of more use to me (I could see it).
July 15th, 2005 at 9:43 am
[...] Astronomers have discovered a planet that has three suns, something that was long thought to be impossible. (Astronomers argued that the orbits would be too unstable.) Can a planet in a figure eight orbit be far behind? [...]
June 15th, 2006 at 11:02 pm
[...] Week 234 of John Baez’ This Week in Mathematical Physics is up. Most of this week’s edition is about the relationship of mathematics and music, but he does touch on a topic we’ve discussed before: weird orbits in classical mechanics. Cris Moore and Michael Nauenberg have found many new and strange solutions to the n-body problem and have provided movies (animated GIFs). The most amazing one is 21 bodies all moving along the same figure eight orbit. [...]