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 Originally Posted by a500lbgorilla
It struck me as a much easier question to ask simply about a very, very small ball of tnt in empty space. Would any of the outer most bits move to infinity after detonation?
I didn't do the work to figure out how TNT actually works, but it seems to be the most sensible angle of attack.
This was fun.
escape velocity = sqrt(2*G*M/r)
where G = 6.67(10)^-11 m^3/(kg s^2), M is the mass from which escape is happening, and r is the distance from that center of mass.
The mass of a sphere is M = 4/3*pi*r^3*rho, where rho is the density.
Substituting into the first equation,
escape velocity = sqrt(2*G*(4/3*pi*r^3*rho)/r)
escape velocity = sqrt(8/3*G*pi*r^2*rho)
escape velocity = 2*r*sqrt(2/3*G*pi*rho)
Solve for r.
r = {escape velocity}/(2*sqrt(2/3*G*pi*rho))
Plugging in the detonation velocity of TNT (6,900 m/s) as the escape velocity, and the density of TNT for rho (1654 kg/m^3), we can solve for the critical radius of TNT which would have escape velocity equal to the detonation velocity.
r = 7.18 million meters
So a ball of TNT which is 14,355 km (~9,000 miles) in diameter would be just big enough to keep itself mostly not escaping to infinity when it blows up. Any smaller and the surface bits would be escaping to infinity. The bits deeper inside have lower escape velocity, but further up the gravity well to go. Since they start with the same 6,900 m/s, and they would lose velocity as they move upward in the gravitational field, they would decelerate and therefore would not have enough velocity to escape.
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