http://www.myphysicslab.com/collision.html ----- Original Message ----- From: "R. William Gosper" <rwg@spnet.com> To: <math-fun@mailman.xmission.com> Cc: <vvmih@ukrpack.net> Sent: Friday, June 27, 2003 8:52 PM Subject: [math-fun] triple star
http://www.freewebz.com/vitaliy/triApplet/triGrav.html is an interesting three-body simulation applet with colored, fading trails. Unfortunately, you don't get to play with the initial conditions, which are equal (point) masses, zero net momentum, zero net angular momentum (wrt origin), fixed or slightly randomized initial positions, and slightly randomized initial velocities. Chaos quickly magnifies the initial perturbations into qualitatively different runs.
The bodies spend some of their time "braiding", but most of their time approximating two "two body problems", with a pair of bodies in a tight orbit simulating a double mass about which the third body describes a larger orbit that frequently crosses the screen boundaries. However, due to the zero initial angular momentum, these larger orbits are highly eccentric and terminate after only one period in a sort of "elastic collision" which shuffles the orbital relationships.
Sooner or later you have to restart because one of these collisions leaves two bodies in such a tight, low energy orbit that the liberated kinetic energy imparts the third body with escape velocity, the tight pair flying off in the opposite direction. (Occasionally, there is not quite escape velocity, and the bodies return after several minutes.)
So why don't triple star systems fly apart, too? One obvious difference is that "collisions" are vastly less frequent in 3-space than 2-space. Another is that heavenly masses are typically highly unequal (e.g., Sun, Earth, Moon). Another possibility is spurious energy buildup in the simulation from accumulated Runge-Kutta errors. A sensitive test of this would be if we could initialize to the recently discovered (barely) stable braiding orbit.
But I think the main source of instability is the absence of net angular momentum. My guess is that the author nulled out the angular momentum because stability is visually boring compared to braiding and "colliding", even at the cost of impermanence. Or perhaps someone has found a chaotic triple star that proves me wrong? --rwg PS: Does anyone know of tumbling brick/asteroid animation on the Web?
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