Conservation of Angular Momentum
Most recent answer: 08/05/2016
- Ohad Frand (age 39)
The total torque is exactly zero. In general that's true for any closed system- angular momentum is conserved. In general, however, you have to include electromagnetic fields and other non-obvious components of the angular momentum. In this case, with purely central forces between the masses, the obvious angular momentum from their motions is conserved, with no need for other terms.
The proof is essentially the one Newton used to explain Kepler's Second Law. Newton's Third Law furantees that the forces in any pair are equal and opposite. Since they are along the line of centers between the two objects in the pair, they have equal lever arms around any point and thus give zero net torque.
Numerical simulations have a little jitter from the finite time intervals and from rounding errors. So the numerical answers aren't exact.
(published on 08/05/2016)