Aren't there better solutions? For functional satellites, of course, you could just de-orbit them (so that they burn while re-entering the Earth's atmosphere), but even for passive objects, maybe you could steer them so that they start falling towards the earth. The Wikipedia article on Kessler Syndrome[1] suggest using lasers, but I guess other ways are possible: if you intend to "blow them up", you might as well redirect the rocket to explode slightly above the orbiting object, so that it is not damaged, but only pushed towards the Earth.

[1]: http://en.wikipedia.org/wiki/Kessler_syndrome

There are some orbital mechanics problems. You can't "steer" in orbit. Shoving down at any sane rate results in going up half an orbit later. The best place to blow it up would be in front of it. A couple hundred m/s is all it takes in some cases.

There's a free windows only game called Orbiter under continuous (ish) development since early 2000s. Its informative about the weird truths of orbital dynamics. Several years ago I went thru a phase of flying between Jupiters moons for fun.

There's probably a startup idea in creating what amounts to a E6B for orbital mechanics. The problem is making it elegant and easy to use. Anybody can open matlab/octave/mathematica/whatever and say "just enter a bunch of equations". I'm not sure the MFDs in orbiter are the wave of the future either. And its easy to get sucked into the trap of making it too simple for the .edu market such that it can't actually simulate anything. Its a hard problem. Maybe more for a PHD project because I'm mystified how to monetize.

One day we're going to need Kessler Cleaners in high geosync orbits to use lasers to "encourage" debris to deorbit.