UAH > Math > Colloquia > 11/3/2006
When a macroscopic piece of matter collides with a target at a relative velocity that exceeds the speed of sound in the target, a flash of impact radiation occurs. In the solar system, such collisions occur when chunks of matter ejected by comets are accelerated by the gravitational fields of the sun and the planets to kinetic energies high enough to excite radiation upon collision with another planetary object. The encounter between the Shoemaker-Levy 9 comet and Jupiter in 1994 is an example. On earth, macroscopic pieces of matter can be accelerated to similar kinetic energies by hydrogen gas guns. The mechanics of collision are determined by the Rankine-Hugoniot equations of shock wave theory. The wavelength distribution of this impact radiation is ordinarily represented by a Planck spectrum. Using only algebraic manipulation, we will solve the equations of mechanics and radiation to obtain the relation between the total radiated power and in the velocity of impact. Under the assumption that the relative kinetic energy of the collision is converted into heat through the heat capacity of the objects involved in the collision, we find that the radiated power is proportional to the eight power of the impact velocity.[1]