Asteroid collision debris calculation I wonder how to determine the directions, in which the collision debris is launched when 2 asteroids collide.
I am aware of: m1*v1 + m2*v2 = m*v = m3*v3 + m4*v4 + m5*v5 + ...
and this works just fine for the masses and valocity, however I find it difficult to determine the boundaries of the directions and under what circumstances shatter be produced or the asteroids will just "merge". 
All info is appreciated :)
 A: I think that this problem doesn't have an exact answer. Some time ago, I talked about this with the astrophysicist Paolicchi (this is the asteroid named after him) who works on the field. The conclusion is that debris are produced at random and you can only impose some ("few") constraints globally, say on big branches of the asteroids belt or of planetary ring. There debris "termalize" after a big number of collision and remain at rest with respect to each others. In the case of just a collision the physics is complicated... I list just some points:


*

*the asteroids are typically non-self-gravitating objects, that is they're mainly taken together by (local) electric forces. Hence, they are not round and, typically, they doesn't merge, since matter globally is electrically neutral. The same is true for artificial asteroids;

*since they spin and they have complex shapes their collisions are very difficult to modelize. You can apply the conservation of momenta but you have no boundaries on the velocities of each single fragment;

*for some purposes, it could be useful to approximate the production of debris as proportional to the energy  in the center of mass of the two colliding asteroids: $E_{\text{cm}}\propto n$ of fragments. Then assume a $n$-body decay, each with the same mass. Even in the case of $n\gtrsim 3$, you can only have a phase-space for these debris and some probability density functions for their production angles.

