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Can someone define for me the distribution of matter from an explosion in a vacuum far from any gravitational sources of influence please?

 

How powerful is the explosion comparable to the force of gravity? In order to get an answer, I'll take the limit of a very powerful explosion symmetrically scattering lots of very lot particles. Furthermore, lets take the initial shape to be a spherical shell of some radius R. Now, the total mass in our system is constant (in the non-relativistic limit). So, we expect as the shell moves outward that:

 

4*pi*r^2 *S= M

or

S = M/(4*pi*r^2). Here, M is the total mass, r is the current radius of the shell. S is the mass/area that we are looking for.

 

If you want the distribution as a function of time, replace r with the velocity of particles and the time. If you want an object with volume instead of a shell, build your sphere out of symmetric shells. Hope that helps.

-Will

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